RD SHARMA Solutions for Class 9 Maths Chapter 24 - Measures of Central Tendency

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Chapter 24 - Measures of Central Tendency Exercise 24.21

Question 1

Which one of the following is not a measure of central value?

(a) Mean

(b) Range

(c) Median

(d) Mode

Solution 1

Range is not a measure of central value.

The difference between the highest value and the lowest value in the data set is called Range.

Hence, correct option is (b).

Question 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Chapter 24 - Measures of Central Tendency Exercise 24.22

Question 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 2

The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers is 78. The value of discarded number is

(a) 98

(b) 99

(c) 100

(d) 101

Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 3

For which set of numbers do the mean, median and mode all have the same value?

(a) 2, 2, 2, 2, 4

(b) 1, 3, 3, 3, 5

(c) 1, 1, 2, 5, 6

(d) 1, 1, 1, 2, 5

Solution 3

 

  Mean Median Mode
2, 2, 2, 2, 4 12/5 = 2.4  2 2
1, 3, 3, 3, 5 15/5 = 3 3 3
1, 1, 2, 5, 6 15/5 = 3 2 1
1, 1, 1, 2, 5 10/5 = 2 1 1

From above table, data 1, 3, 3, 3, 5 has mean, median, mode all have same value, i.e. 3.

Hence, correct option is (b).

Question 4

For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?

(a) Mean = Median

(b) Mean > Mode

(c) Mean < Mode

(d) Mode = Median

Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 5

If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value of x is

(a) 10

(b) 12

(c) 14

(d) 16

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 6

If the mean of five observations x, x + 2, x + 4, x + 6, x + 8, is 11, then the mean of first three observations is

(a) 9

(b) 11

(c) 13

(d) none of these

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 7

Mode is

(a) least frequent value

(b) middle most value

(c) most frequent value

(d) none of these

Solution 7

Most Frequent value is called mode.

Hence, correct option is (c).

Question 8

The following is the data of wages per day: 5, 4, 7, 5, 8, 8, 8, 5, 7, 9, 5, 7, 9, 10, 8

The mode of the data is

(a) 7

(b) 5

(c) 8

(d) 10

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 9

The median of the following data: 0, 2, 2, 2, -3, 5, -1, 5, 5, -3, 6, 6, 5, 6 is

(a) 0

(b) -1.5

(c) 2

(d) 3.5

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 10

The algebraic sum of the deviations of a set of n values from their mean is

(a) 0

(b) n - 1

(c) n

(d) n + 1

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 11

A, B, C are three sets of values of x:

A: 2, 3, 7, 1, 3, 2, 3

B: 7, 5, 9, 12, 5, 3, 8

C: 4, 4, 11, 7, 2, 3, 4

Which one of the following statements is correct?

(a) Mean of A = Mode of C

(b) Mean of C = Median of B

(c) Median of B = Mode of A

(d) Mean, Median and Mode of A are equal.

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 12

The empirical relation between mean, mode and median is

(a) Mode = 3 Median - 2 Mean

(b) Mode = 2 Median - 3 Mean

(c) Median = 3 Mode - 2 Mean

(d) Mean = 3 Median - 2 Mode

Solution 12

The empirical Relation between mean, median and mode is

Mode = 3 Median - 2 mean

Hence, correct option is (a).

Question 13

The mean of a, b, c, d and e is 28. If the mean of a, c, and e is 24, what is the mean of b and d?

(a) 31

(b) 32

(c) 33

(d) 34

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Chapter 24 - Measures of Central Tendency Exercise Ex. 24.1

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 7
Find the mean of first five multiples of 3.
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 10

The numbers of children in 10 families of a locality are:

2, 4, 3, 4, 2, 0, 3, 5, 1, 1, 5. Find the mean number of children per family.

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 12

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 13

The traffic police recorded the speed (in km/hr) of 10 motorists as 47, 53, 49, 60, 39, 42, 55, 57, 52, 48. Later on an error in recording instrument was found. Find the correct average speed of the motorists if the instrument recorded 5 km/hr less in each case.

Solution 13

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 14

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 15

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 16

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 17

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 18

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 19

If M is the mean of x1, x2, x3, x4, x5 and x6 , prove that

(x1 - M) + (x2 - M) + (x3 -M) + (x4 - M) + (x- M) + (x6 - M) = 0

Solution 19

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 20

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 21
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 21
(i)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

(ii)

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 22
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 22
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 23
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 23
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 24
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 24
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Chapter 24 - Measures of Central Tendency Exercise Ex. 24.2

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 4

Five coins were simultaneously tossed 1000 times and at each toss the number of heads were observed. The number of tosses during which 0, 1, 2, 3, 4 and 5 heads were obtained are shown in the table below. Find the mean number of heads per toss.

No. of heads per toss No. of tosses
0

1

2

3

4

5

38

144

342

287

164

25
Total 1000



Solution 4

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 7

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 8

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 9

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 10

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Solution 11

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 12
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 12
x f xf
10 17 170
30 f1 30f1
50 32 1600
70 f2 70f2
90 19 1710
  N = 120 Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency


Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Chapter 24 - Measures of Central Tendency Exercise Ex. 24.3

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 4
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 6
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 7
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 8
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 9
Numbers 50, 42, 35, 2x + 10, 2x - 8, 12, 11, 8 are written in descending order and their median is 25, find x.
Solution 9
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 10
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 11
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 11
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 12
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 12
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Question 13
The following observations have been arranged in ascending order. If the median of the data is 63, find the value of x.
    29,    32,    48,    50,    x,    x + 2,    72,    78,    84,    95    

Solution 13
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Chapter 24 - Measures of Central Tendency Exercise Ex. 24.4

Question 1
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 1

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 2
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 2

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 3
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 3

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 4
Find the mode of
        14,      25,    14,    28,    18,    17,    18,    14,    23,    22,    14,    18
Solution 4
Arranging the data in an ascending order 
14, 14, 14, 14, 17, 18, 18, 18, 22, 23, 25, 28  
Here observation 14 is having the highest frequency i.e. 4 in given data. So, mode of given data is 14.  

Question 5
Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency
Solution 5

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

Question 6

The demand of different sizes, as obtained by a survey, is given below:

Size 38 39 40 41 42 43 44 Total
Number of persons (wearing it): 26 39 20 15 13 7 5 125


Find the modal shirt size, as observed from the survey.

Solution 6

Rd-sharma Solutions Cbse Class 9 Mathematics Chapter - Measures Of Central Tendency

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