RD SHARMA Solutions for Class 10 Maths Chapter 15 - Statistics

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Chapter 15 - Statistics Exercise 15.66

Question 1

Which of the following is not a measure of central tendency?

(a) Mean

(b) Median

(c) Mode

(d) Standard deviation

Solution 1

There are three main measure of central tendency the mode, the median and the mean.

Each of these measures describes a different indication of the typical or central value in the distribution.

The mode is the most commonly occuring value in a distribution.

Median is middle value of distribution.

While standard deviation is a measure of dispersion of a set of data from its mean.

So, the correct option is (d).

Question 2

The algebraic sum of deviations of a frequency distribution from its mean is

(a) always positive

(b) always negative

(c) 0

(d) a non-zero number

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

For a frequency distribution, mean, median and mode are connected by the relation

(a) Mode = 3 mean - 2 median

(b) Mode = 2 median - 3 mean

(c) Mode = 3 median - 2 mean

(d) Mode = 3 median + 2 mean

Solution 4

It is well known that relation between mean, median and mode 1 s

3 median = mode + 2 mean

Mode = 3 median - 2 mean

So, the correct option is (a).

Question 5

Which of the following cannot be determined graphically?

(a) Mean

(b) Median

(c) Mode

(d) None of these

Solution 5

Mean is an average value of any given data which cannot be determined by a graph.

Value of median and mode can easily be calculated by graph.

Median is middle value of a distribution and mode is highest frequent value of a given distribution.

So, the correct option is (a).

Question 6

The median of a given frequency distribution is found graphically with the help of

(a) Histogram

(b) Frequency curve

(c) Frequency polygon

(d) Ogive

Solution 6

The median of a series may be determined through the graphical presentation of data in the forms of Ogives.

Ogive is a curve showing the cummulative frequency for a given set of data.

To get the median we present the data graphically in the form of 'less than' ogive  or 'more than' ogive

Then the point of intersection of the two graphs gives the value of the median.

So, the correct option is (d).

Question 7

The mode of a frequency distribution can be detremined graphically from

(a) Histogram

(b) frequency polygon

(c) ogive

(d) frequency curve

Solution 7

Histogram is used to plot the distribution of numerical data or frequency of occurrences of data.

Mode is the most commonly occurring value in the data.

So in distribution or Histogram, the value of the x-coordinate corresponding to the peak value on y - axis, is the mode.

So, the correct option is (a).

Question 8

Mode is

(a) least frequent value

(b) middle most value

(c) most frequent value

(d) None of these

Solution 8

Mode is the most frequent value in the data.

Mode is the value which occurs the most number of times.

So, the correct option is (c).

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 10

One of the methods of determining mode is

(a) Mode = 2 median - 3 Mean

(b) Mode = 2 Median + 3 Mean

(c) Mode = 3 Median - 2 Mean

(d) Mode = 3 Median + 2 Mean

Solution 10

We know that the relation between mean, median & mode is

3 Median = Mode + 2 Mean

Hence, Mode = 3 Median - 2 Mean

So, the correct option is (c).

Chapter 15 - Statistics Exercise 15.67

Question 1

If the mean of the following distribution is 2.6, then the value of y is

Variable (y) : 1   2   3   4   5

Frequency :   4   5    y   1   2

(a) 3    (b) 8     (c) 13    (d) 24

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

The relationship between mean, median and mode for a moderately skewed distribution is

(a) Mode = 2 Median - 3 Mean

(b) Mode = Median - 2 Mean

(c) Mode = 2 Median - Mean

(d) Mode = 3 Median - 2 mean

Solution 2

We know that the relation between mean, median & mode is

3 Median = mode + 2 Mean

Hence, mode = 3 Median - 2 Mean

So, the correct option is (d).

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

If the arithmetic mean of xx +3 , x + 6, x + 9, x + 12 is 10, then x =

(a) 1

(b) 2

(c) 6

(d) 4

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 5

If the median of the data : 24, 25, 26, x + 2, x + 3, 30, 31, 34 is 27.5 then x =

(a) 27

(b) 25

(c) 28

(d) 30

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

If the median of the data: 6, 7, x - 2, x, 17, 20 written in ascending order, is 16. Then x =

(a) 15

(b) 16

(c) 17

(d) 18

 

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

The median of first 10 prime numbers is

(a) 11

(b) 12

(c) 13

(d) 14

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 8

If the mode of the data : 64, 60, 48, x, 43, 48, 43, 34 is 43 then x + 3 =

(a) 44

(b) 45

(c) 46

(d) 48

 

Solution 8

Mode is the number in observation data is that which repeats most number of time

In the given data 48 comes twice and 43 comes twice but mode is 43.

Hence if x = 43 then 43 comes thrice.

So x + 3 = 43 + 3 = 46

So, the correct option is (c).

Question 9

If the mode of the data : 16, 15, 17, 16, 15, x, 19, 17, 14 is 15 then x =

(a) 15

(b) 16

(c) 17

(d) 19

Solution 9

In the given data 15, 16, 17 comes twice but given 15 is mode.

Hence 15 comes more than 16, 17.

This is only possible if x = 15.

So, the correct option is (a).

Question 10

The mean of 1, 3, 4, 5, 7, 4 is m. The numbers 3, 2, 2, 4, 3, 3, p have mean m - 1 and median q. Then, p + q =

(a) 4

(b) 5

(c) 6

(d) 7

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 12

If the mean of 6, 7, x , 8, y, 14 is 9, then

(a) x + y = 21

(b) x + y = 19

(c) x - y = 19

(d) x - y = 21

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise 15.68

Question 1

The arithmetic mean and mode of a data are 24 and 12 respectively, then its median is

(a) 25

(b) 18

(c) 20

(d) 22

Solution 1

We know, 3 Median = Mode + 2 Mean

mean = 24

mode = 12

3 median = 12 + 2 × 24

              = 12 + 48

              = 60

median = 20

So, the correct option is (c).

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

If the difference of mode and median of a data is 24, then the difference of median and mean is

(a) 12

(b) 24

(c) 8

(d) 36

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 5

If the arithmetic mean of 7, 8, x, 11, 14 is x then x = 

(a) 1

(b) 9.5

(c) 10

(d) 10.5

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

If mode of a series exceeds its mean by 12, then mode exceeds the median by

(a) 4

(b) 8

(c) 6

(d) 10

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

If the mean of first n natural number is 15, then  n =

(a) 15

(b) 30

(c) 14

(d) 29

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 11

If 35 is removed from the data: 30, 34, 35, 36, 37, 38, 39, 40, then the median increases by

(a) 2

(b) 1.5

(c) 1

(d) 0.5

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 12

While computing mean of grouped data, we assume that the frequencies are

 

a. evenly distributed over all the classes.

b. centred at the class marks of the classes.

c. centred at the upper limit of the classes.

d. centred at the lower limit of the classes.

Solution 12

While computing the mean of the grouped data, we assume that the frequencies are centred at the class marks of the classes.

Hence, correct option is (b).

Question 13

In the formula Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics, for finding the mean of grouped frequency distribution ui =

 

 

a. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

b. h(xi - a)

c. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

d. Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise 15.69

Question 1

For the following distribution:

 

Class:

0-5

5-10

10-15

15-20

20-25

Frequency:

10

15

12

20

9

The sum of the lower limits of the median and modal class is

 

a. 15

b. 25

c. 30

d. 35

 

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

For the following distribution:

 

Below:

10

20

30

40

50

60

Number of students:

3

12

27

57

75

80

 

The model class is

 

a. 10-20

b. 20-30

c. 30-40

d. 50-60

 

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 3

Consider the following frequency distribution:

 

Class:

65-85

85-105

105-125

125-145

145-165

165-185

185-205

Frequency:

4

5

13

20

14

7

4

The difference of the upper limit of the median class and the lower limit of the modal class is

 

a. 0

b. 19

c. 20

d. 38

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

In the formula Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics, for finding the mean of grouped data dis are deviations from a of

 

a. Lower limits of classes

b. Upper limits of classes

c. Mid-points of classes

d. Frequency of the class marks

Solution 4

di's are the deviations from a of mid-points of classes.

Hence, correct option is (c).

Question 5

The abscissa of the point of intersection of less than type and of the more than type cumulative frequency curves of a grouped data given its

 

a. Mean

b. Median

c. Mode

d. All the three above

Solution 5

The abscissa of the point of intersection of less than type and of the more than type cumulative frequency curves of a grouped data given its median.

Hence, correct option is (b).

 

Question 6

Consider the following frequency distribution:

 

Class:

0-5

6-11

12-17

18-23

24-29

Frequency:

13

10

15

8

11

The upper limit of the median class is

 

a. 17

b. 17.5

c. 18

d. 18.5

 

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise Ex. 15.1

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 11

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

 

 

 

 

 

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise Ex. 15.2

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise Ex. 15.3

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Number of plants 0 - 2 2 - 4 4 - 6 6 - 8 8 - 10 10 - 12 12 - 14
Number of houses 1 2 1 5 6 2 3



Which method did you use for finding the mean, and why?

Solution 2

Let us find class marks (xi) for each interval by using the relation.
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Now we may compute xi and fixias following

Number of plants Number of houses (fi) xi fixi
0 - 2 1 1 1 x 1 = 1
2 - 4 2 3 2 x 3 = 6
4 - 6 1 5 1 x 5 = 5
6 - 8 5 7 5 x 7 = 35
8 - 10 6 9 6 x 9 = 54
10 - 12 2 11 2 x 11 = 22
12 - 14 3 13 3 x 13 = 39
Total 20   162



From the table we may observe that
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics 

So, mean number of plants per house is 8.1.
We have used here direct method as values of class marks (xi) and fi are small.

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Fine the mean heart beats per minute for these women, choosing a suitable method.

Number of heart beats per minute 65 - 68 68 - 71
71-74
74 - 77 77 - 80 80 - 83 83 - 86
Number of women 2 4 3 8 7 4 2
Solution 4

We may find class mark of each interval (xi) by using the relation.
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Class size h of this data = 3
Now taking 75.5 as assumed mean (a) we may calculate di, ui, fiui as following.

Number of heart beats per minute Number of women fi xi di = xi -75.5 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics fiui
65 - 68 2 66.5 - 9 - 3 - 6
68 - 71 4 69.5 - 6 - 2 - 8
71 - 74 3 72.5 - 3 - 1 - 3
74 - 77 8 75.5 0 0 0
77 - 80 7 78.5 3 1 7
80 - 83 4 81.5 6 2 8
83 - 86 2 84.5 9 3 6
Total 30       4


Now we may observe from table that
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So mean hear beats per minute for these women are 75.9 beats per minute.

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 8

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 9

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 10

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 11

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 12

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 13

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 14

Find the mean of the following frequency distribution:

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 15

For the following distribution, calculate mean using all suitable methods :

Size of item 1-4 4-9 9-16 16-27
Frequency 6 12 26 20

 

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 18

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 19

The following distribution shows the daily pocket allowance given to the children of a multistorey building. The average pocket allowance is Rs 18.00. Find out the missing frequency.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 19

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 21

In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.

Number of mangoes 50 - 52 53 - 55 56 - 58 59 - 61 62 - 64
Number of boxes 15 110 135 115 25



Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Solution 21
Number of mangoes Number of boxes
fi
50 - 52 15
53 - 55 110
56 - 58 135
59 - 61 115
62 - 64 25


We may observe that class intervals are not continuous. There is a gap of 1 between two class intervals. So we have to add Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics to upper class limit and subtract Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics from lower class limit of each interval.
And class mark (xi) may be obtained by using the relation
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Class size (h) of this data = 3

Now taking 57 as assumed mean (a) we may calculate di, ui, fiui as follows:

 

Class interval fi xi di = xi - 57 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics fiui
49.5 - 52.5 15 51 -6 -2 -30
52.5 - 55.5 110 54 -3 -1 -110
55.5 - 58.5 135 57 0 0 0
58.5 - 61.5 115 60 3 1 115
61.5 - 64.5 25 63 6 2 50
Total 400       25


Now, we have:
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics 
Clearly mean number of mangoes kept in a packing box is 57.19.

Note: We have chosen step deviation method here as values of fi, di are big and also there is a common multiple between all di.

Question 22

The table below shows the daily expenditure on food of 25 households in a locality.

Daily expenditure (in Rs) 100 - 150 150 - 200 200 - 250 250 - 300 300 - 350
Number of households 4 5 12 2 2


Find the mean daily expenditure on food by a suitable method.

Solution 22

We may calculate class mark (xi) for each interval by using the relation

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Class size = 50

Now taking 225 as assumed mean (a) we may calculate di, ui, fiui as follows:

 

Daily expenditure (in Rs) fi xi di = xi - 225 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics fiui
100 - 150 4 125 -100 -2 -8
150 - 200 5 175 -50 -1 -5
200 - 250 12 225 0 0 0
250 - 300 2 275 50 1 2
300 - 350 2 325 100 2 4
Total         -7


Now we may observe that -

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 23

To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

concentration of SO2 (in ppm) Frequency
0.00 - 0.04 4
0.04 - 0.08 9
0.08 - 0.12 9
0.12 - 0.16 2
0.16 - 0.20 4
0.20 - 0.24 2


Find the mean concentration of SO2 in the air.

Solution 23

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Concentration of SO2 (in ppm) Frequency Class mark xi di = xi - 0.14 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics fiui
0.00 - 0.04 4 0.02 -0.12 -3 -12
0.04 - 0.08 9 0.06 -0.08 -2 -18
0.08 - 0.12 9 0.10 -0.04 -1 -9
0.12 - 0.16 2 0.14 0 0 0
0.16 - 0.20 4 0.18 0.04 1 4
0.20 - 0.24 2 0.22 0.08 2 4
Total 30       -31


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 24

A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.


Number of days

0 - 6

6 - 10

10 - 14

14 - 20

20 - 28

28 - 38

38 - 40

Number of students

11

10

7

4

4

3

1
Solution 24

We may find class mark of each interval by using the relation

 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Now, taking 17 as assumed mean (a) we may calculate di and fidi as follows: 


Number of days

Number of students
fi

xi

di= xi - 17

fidi

0 - 6

11

3

-14

-154

6 -10

10

8

-9

-90

10 - 14

7

12

-5

-35

14 - 20

4

17

0

0

20 - 28

4

24

7

28

28 - 38

3

33

16

48

38 - 40

1

39

22

22

Total

40





-181



Now we may observe that
 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So, mean number of days is 12.475 days, for which a student was absent.

Question 25

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.


Literacy rate
(in %)

45 - 55

55 - 65

65 - 75

75 - 85

85 - 95

Number of cities

3

10

11

8

3
Solution 25

We may find class marks by using the relation

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Class size (h) for this data = 10

Now taking 70 as assumed mean (a) we may calculate di, ui, and fiui as follows:  


Literacy rate
(in %)

Number of cities
fi

xi

di= xi - 70

ui =di/10

fiui

45 - 55

3


50

-20

-2

-6

55 - 65

10

60

-10

-1

-10

65 - 75

11

70

0

0

0

75 - 85

8

80

10

1

8


85 - 95

3

90

20

2

6

Total

35







-2



Now we may observe that
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So, mean literacy rate is 69.43%.

Question 26

The following is the cumulative frequency distribution (of less than type) of 1000 persons each of age 20 years and above. Determine the mean age.

 

Age below (in years)

30

40

50

60

70

80

Number of persons

100

220

350

750

950

1000

 

Solution 26

Here, we have cumulative frequency distribution less than type. First we convert it into an ordinary frequency distribution.

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 27

If the means of the following frequency distribution is 18, find the missing frequency.

 

Class interval:

11-13

13-15

15-17

17-19

19-21

21-23

23-25

Frequency:

3

6

9

13

f

5

4

 

Solution 27

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 28

Find the missing frequencies in the following distribution, if the sum of the frequencies is 120 and the mean is 50.

 

Class:

0-20

20-40

40-60

60-80

80-100

Frequency:

17

f1

32

f2

19

 

Solution 28

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 29

The daily income of a sample of 50 employees are tabulated as follows:

 

Income (in Rs.):

1-200

201-400

401-600

601-800

No. of employees:

14

15

14

7

 

Find the mean daily income of employees.

Solution 29

 Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise Ex. 15.4

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

The median height of the students is Rs 167.13.

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 8

Find the following tables gives the distribution of the life time of 400 neon lamps:


Life time (in hours)

Number of lamps

1500 - 2000

14

2000 - 2500

56

2500 - 3000

60

3000 - 3500

86

3500 - 4000

74

4000 - 4500

62

4500 - 5000

48



Find the median life time of a lamp.

Solution 8

We can find cumulative frequencies with their respective class intervals as below -


Life time

Number of lamps (fi)

Cumulative frequency

1500 - 2000

14

14

2000 - 2500

56

14 + 56 = 70

2500 - 3000

60

70 + 60 = 130

3000 - 3500

86

130 + 86 = 216

3500 - 4000

74

216 + 74 = 290

4000 - 4500

62

290 + 62 = 352

4500 - 5000

48

352 + 48 = 400

Total (n)

400
 



Now we may observe that cumulative frequency just greater than Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics is 216 belonging to class interval 3000 - 3500.
Median class = 3000 - 3500
Lower limit (l) of median class = 3000
Frequency (f) of median class = 86
Cumulative frequency (cf) of class preceding median class = 130
Class size (h) = 500

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So, median life time of lamps is 3406.98 hours.

Question 9

The distribution below gives the weights of 30 students of a class. Find the median weight of the students.


Weight
(in kg)

40 - 45

45 - 50

50 - 55

55 - 60

60 - 65

65 - 70

70 - 75

Number of students

2


3

8

6

6

3

2
Solution 9

We may find cumulative frequencies with their respective class intervals as below

Weight (in kg) 40 - 45 45 - 50 50 - 55 55 - 60 60 - 65 65 - 70 70 - 75
Number of students (f) 2 3 8 6 6 3 2
c.f. 2 5 13 19 25 28 30


Cumulative frequency just greater than Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics  is 19, belonging to class interval 55 - 60.
Median class = 55 - 60
Lower limit (l) of median class = 55
Frequency (f) of median class = 6
Cumulative frequency (cf) of median class = 13
Class size (h) = 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

So, median weight is 56.67 kg.

Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

You are given that the median value is 46 and the total number of items is 230.
(i) Using the median formula fill up missing frequencies.
(ii) Calculate the AM of the completed distribution.
Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Question 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 12

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 14

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 18

A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 year.


Age (in years)

Number of policy holders

Below 20

2

Below 25

6

Below 30

24

Below 35

45

Below 40

78

Below 45

89

Below 50

92

Below 55

98

Below 60

100
Solution 18

Here class width is not same. There is no need to adjust the frequencies according to class intervals. Now given frequency table is of less than type represented with upper class limits. As policies were given only to persons having age 18 years onwards but less than 60 years, we can define class intervals with their respective cumulative frequency as below


Age (in years)

Number of policy holders (fi)

Cumulative frequency (cf)

18 - 20

2

2

20 - 25

6 - 2 = 4

6

25 - 30

24 - 6 = 18

24

30 - 35

45 - 24 = 21

45

35 - 40

78 - 45 = 33

78

40 - 45

89 - 78 = 11

89
45 - 50
92 - 89 = 3

92

50 - 55

98 - 92 = 6

98

55 - 60

100 - 98 = 2

100

Total (n)

 





Now from table we may observe that n = 100.

Cumulative frequency (cf) just greater than Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics is 78 belonging to interval 35 - 40
So, median class = 35 - 40
Lower limit (l) of median class = 35
Class size (h) = 5
Frequency (f) of median class = 33
Cumulative frequency (cf) of class preceding median class = 45

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So, median age is 35.76 years.

Question 19

The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:


Length (in mm)

Number or leaves fi

118 - 126

3

127 - 135

5

136 - 144

9

145 - 153

12

154 - 162

5

163 - 171

4

172 - 180

2



Find the median length of the leaves.

Solution 19

The given data is not having continuous class intervals. We can observe that difference between two class intervals is 1. So, we have to add and subtract

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics  to upper class limits and lower class limits.
Now continuous class intervals with respective cumulative frequencies can be represented as below:

 


Length (in mm)

Number or leaves fi

Cumulative frequency

117.5 - 126.5

3

3

126.5 - 135.5

5

3 + 5 = 8

135.5 - 144.5

9

 


8 + 9 = 17

144.5 - 153.5

12

17 + 12 = 29

153.5 - 162.5

5

 


29 + 5 = 34

162.5 - 171.5

4

34 + 4 = 38

171.5 - 180.5

2

38 + 2 = 40



From the table we may observe that cumulative frequency just greater then
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics  is 29, belonging to class interval 144.5 - 153.5.
Median class = 144.5 - 153.5
Lower limit (l) of median class = 144.5
Class size (h) = 9
Frequency (f) of median class = 12
Cumulative frequency (cf) of class preceding median class = 17


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So, median length of leaves is 146.75 mm.

Question 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 21

The median of the distribution given below is 14.4. Find the values of x and y, if the total frequency is 20.

 

Class interval:

0-6

6-12

12-18

18-24

24-30

Frequency:

4

x

5

y

1

 

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 22

The median of the following data is 50. Find the values of p and q, if the sum of all the frequencies is 90.

 

Marks:

20-30

30-40

40-50

50-60

60-70

70-80

80-90

Frequency:

p

15

25

20

q

8

10

 

Solution 22

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise Ex. 15.5

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 8

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 9

The following table shows the ages of the patients admitted in a hospital during a year:


Age (in years)

5 - 15

15 - 25

25 - 35

35 - 45

45 - 55

55 - 65

Number of patients

6

11

21

23

14

5



Find the mode and the mean of the data given above. Compare and interpret the two measures of central tendency.

Solution 9

We may compute class marks (xi) as per the relation

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics 
Now taking 30 as assumed mean (a) we may calculate di and fidi as follows.


Age (in years)

Number of patients
fi

class mark
xi

di= xi - 30

fidi

5 - 15

6

10

-20

-120

15 - 25

11

20

-10

-110

25 - 35

21

30

0

0

35 - 45

23

40

10

230

45 - 55

14

50

20

280

55 - 65

5

60

30

150

Total

80





430



From the table we may observe that

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Clearly, mean of this data is 35.38. It represents that on an average the age of a patient admitted to hospital was 35.38 years.
As we may observe that maximum class frequency is 23 belonging to class interval 35 - 45.
So, modal class = 35 - 45
Lower limit (l) of modal class = 35
Frequency (f1) of modal class = 23
Class size (h) = 10
Frequency (f0) of class preceding the modal class = 21
Frequency (f2) of class succeeding the modal class = 14
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Clearly mode is 36.8.It represents that maximum number of patients admitted in hospital were of 36.8 years.

Question 10

The following data gives the information on the observed lifetimes (in hours) of 225 electrical components:


Lifetimes (in hours)

0 - 20

20 - 40

40 - 60

60 - 80

80 - 100

100 - 120

Frequency

10

35

52

61

38

29



Determine the modal lifetimes of the components.

Solution 10

From the data given as above we may observe that maximum class frequency is 61 belonging to class interval 60 - 80.
So, modal class = 60 - 80
Lower class limit (l) of modal class = 60
Frequency (f1) of modal class = 61
Frequency (f0) of class preceding the modal class = 52
Frequency (f2) of class succeeding the modal class = 38
Class size (h) = 20


Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics 
So, modal lifetime of electrical components is 65.625 hours.

Question 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 11

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 12

The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures.


Number of students
per teacher

Number of
states/U.T

15 - 20

3

20 - 25

8

25 - 30

9

30 - 35

10

35 - 40

3

40 - 45

0

45 - 50

0

50 - 55

2
Solution 12

We may observe from the given data that maximum class frequency is 10 belonging to class interval 30 - 35.
So, modal class = 30 - 35
Class size (h) = 5
Lower limit (l) of modal class = 30
Frequency (f1) of modal class = 10
Frequency (f0) of class preceding modal class = 9
Frequency (f2) of class succeeding modal class = 3
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

It represents that most of states/U.T have a teacher - student ratio as 30.6

Now we may find class marks by using the relation

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Now taking 32.5 as assumed mean (a) we may calculate di, ui and fiui as following.


Number of students
per teacher

Number of states/U.T
(fi)

xi

di = xi - 32.5

 ui

fiui

15 - 20

3

17.5

-15

-3

-9

20 - 25

8

22.5

-10

-2

-16

25 - 30

9

27.5

-5

-1

-9

30 - 35

10

32.5

0

0

0

35 - 40

3

37.5

5

1

3

40 - 45

0

42.5

10

2

0

45 - 50

0

47.5

15

3

0

50 - 55

2

52.5

20

4

 


8

Total

35

 

     
-23



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

So mean of data is 29.2
It represents that on an average teacher - student ratio was 29.2.

Question 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 13

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 14

A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarised it in the table given below. Find the mode of the data:


Number
of cars

0 - 10

10 - 20

20 - 30

30 - 40

40 - 50

50 - 6

60 - 70

70 - 80

Frequency

7

14

13

12

20

11

15

8
Solution 14

From the given data we may observe that maximum class frequency is 20 belonging to 40 - 50 class intervals.
So, modal class = 40 - 50
Lower limit (l) of modal class = 40
Frequency (f1) of modal class = 20
Frequency (f0) of class preceding modal class = 12
Frequency (f2) of class succeeding modal class = 11
Class size = 10
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So mode of this data is 44.7 cars.

Question 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 15

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 16

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 17

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 18

The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.


Expenditure
(in Rs)

Number of families

 


1000 - 1500

24

1500 - 2000

40

2000 - 2500

33

2500 - 3000

28

3000 - 3500

30

3500 - 4000

22

4000 - 4500

16

4500 - 5000

7
Solution 18

We may observe from the given data that maximum class frequency is 40 belonging to 1500 - 2000 intervals.
So, modal class = 1500 - 2000
Lower limit (l) of modal class = 1500
Frequency (f1) of modal class = 40
Frequency (f0) of class preceding modal class = 24
Frequency (f2) of class succeeding modal class = 33
Class size (h) = 500

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics 

So modal monthly expenditure was Rs. 1847.83
Now we may find class mark as

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Class size (h) of give data = 500
Now taking 2750 as assumed mean (a) we may calculate di, ui and fiui as follows:


Expenditure
(in Rs)

Number of families

fi


xi

di = xi - 2750

 ui

fiui

 


1000 - 1500

24

1250

-1500

-3

-72

1500 - 2000

40

1750

-1000

-2

-80

2000 - 2500

33

2250

-500

-1

 

 

-33


2500 - 3000

28

2750

0

0

0

3000 - 3500

30

3250

500

1

30

3500 - 4000

22

3750

1000

2

44

4000 - 4500

16

4250

1500

3

48

4500 - 5000

7

4750

2000

4

28

Total

200

 

 

 

-35



Now from table may observe that

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So, mean monthly expenditure was Rs. 2662.50.

Question 19

The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches.

Runs scored
No of batsman

3000 - 4000

4

4000 - 5000

18

5000 - 6000

9

6000 - 7000

7

7000 - 8000

6

8000 - 9000

3

9000 -10000

1

10000 - 11000

1



Find the mode of the data.

Solution 19

From the given data we may observe that maximum class frequency is 18 belonging to class interval 4000 - 5000.
So, modal class = 4000 - 5000
Lower limit (l) of modal class = 4000
Frequency (f1) of modal class = 18
Frequency (f0) of class preceding modal class = 4
Frequency (f2) of class succeeding modal class = 9
Class size (h) = 1000
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
So mode of given data is 4608.7 runs.

Question 20

The frequency distribution table of agriculture holdings in a village is given below:

 

Area of land (in hectares):

1-3

3-5

5-7

7-9

9-11

11-13

Number of families:

20

45

80

55

40

12

Find the modal agriculture holdings of the village.

Solution 20

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 21

The monthly income of 100 families are given as below:

 

Income in (in Rs.)

Number of families

0-5000

8

5000-10000

26

10000-15000

41

15000-20000

16

20000-25000

3

25000-30000

3

30000-35000

2

35000-40000

1

Calculate the modal income.

Solution 21

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Chapter 15 - Statistics Exercise Ex. 15.6

Question 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 1

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 2

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 3

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 4

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Solution 5

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 6

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics



Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Question 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Solution 7

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Question 8

The annual rainfall record of a city for 66 days if given in the following table:

 

Rainfall (in cm):

0-10

10-20

20-30

30-40

40-50

50-60

Number of days:

22

10

8

15

5

6

Calculate the median rainfall using ogives of more than type and less than type.

 

Solution 8

Less Than Series:

Class interval

Cumulative Frequency

Less than 10

22

Less than 20

32

Less than 30

40

Less than 40

55

Less than 50

60

Less than 60

66

 

We plot the points (10, 22), (20, 32), (30, 40), (40, 55), (50, 60) and (60, 66) to get 'less than type' ogive.

 

More Than Series:

Class interval

Frequency

More than 0

66

More than 10

44

More than 20

34

More than 30

26

More than 40

11

More than 50

6

 

We plot the points (0, 66), (10, 44), (20, 24), (30, 26), (40, 11), and (50, 6) to get more than ogive.

 

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

From the graph, median = 21.25 cm

Question 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 9

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics
Question 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

Solution 10

Rd-sharma Solutions Cbse Class 10 Mathematics Chapter - Statistics

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