NCERT Solutions for Class 9 Maths Chapter 14 - Statistics

Chapter 14 - Statistics Exercise Ex. 14.1

Solution 1
In our day to day life we may collect data in various ways; a few of them have been mentioned here.

    1.    Number of females per 1000 males in various states of our country.
    2.    Height and Weights of students of our class.
    3.    Temperature of past 10 days in our city.
    4.    Number of plants in our locality.
    5.    Rain fall in our city.
    6.    Marks obtained by students of the class in a test.
    7.    Date of birth of students.
    8.    Subjects taught in various schools in class X.  

Solution 2
We know that the information which is collected by the investigator himself with a definite objective in his mind is primary data, whereas when the information is gathered from a source which already had the information stored, is called as secondary data. Now we may observe that the data in 1, 3, and 5 is secondary data and all others are primary data.

Chapter 14 - Statistics Exercise Ex. 14.2

Solution 1
Here, 9 students  have blood groups  A, 6 as B, 3 as AB and 12 as O.
So, the table representing the data is as follows:  

Blood group

Number of students

A

9

B

6

AB

3

O

12

Total

30



As 12 students have the blood group O and 3 have their blood group as AB, clearly that the most common blood group and the rarest blood group among these students is O and AB respectively.
Solution 2
Given that we have to construct a grouped frequency distribution table of class size 5. So, the  class intervals will be as 0 - 5, 5 - 10, 10 - 15, 15 - 20......
Required grouped frequency distribution table as following -
 

Distance (in km)

Tally marks

Number of engineers

0 - 5

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

 5

5 - 10

  Ncert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - Statistics

11

10 -15

   Ncert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - Statistics

11

 15 - 20

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics Ncert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - Statistics

  9

20 - 25

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

  1

25 - 30

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

  1

30 - 35

 Ncert Solutions Cbse Class 9 Mathematics Chapter - StatisticsNcert Solutions Cbse Class 9 Mathematics Chapter - Statistics

  2

Total

 

40

 
 
 
Now  there are only 4 engineers whose homes are at more than or equal to 20 km distance, from their work place.
Most of the engineers are having their workplace up to 15 km distance, from their homes.

Solution 3
(i)    To construct a grouped frequency distribution table of class size 2.
       Class intervals will be as follows 84 - 86, 86 - 88, and 88 - 90... ...
 
        

Relative humidity (in %)

Number of days (frequency )

84 - 86

1

86 - 88

1

88 - 90

2

90 - 92

2

92 - 94

7

94 - 96

6

96 - 98

7

98 - 100

4

Total

30

 
(ii)    Since relative humidity is high so the data must be of a month of rainy season.                       

(iii)    Range of data = maximum value - minimum value
                              = 99.2 - 84.9
                              = 14.3    
Solution 4
(i)    We have to construct a grouped frequency distribution table taking class intervals as 160 - 165, 165 - 170, etc. Now by observing the data given as above we may construct the required table as below -

       

Heights  (in cm)

Number of students (frequency )

150 - 155

12

155 - 160

  9

160 - 165

14

165 - 170

10

170 - 175

  5

Total

50

                                                                                 

(ii)    From the table we can see that  50% of students are shorter than 165 cm.                                                                   

Solution 5
To construct grouped frequency table class intervals to be taken as 0.00 - 0.04, 0.04 - 0.08,

Concentration of SO2  (in ppm)

Number of days (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

Total

30


                                                                                                            
Number of days for which concentration SO2 is more than 0.11 is number of days for which concentration is in between 0.12 - 0.16, 0.16 - 0.20, 0.20 - 0.24.
So, required number of days = 2 + 4 + 2 = 8

Solution 6
By observing the data given above following frequency distribution table can be constructed
 

Number of heads

Number of times (frequency)

0

 6

1

10

2

  9

3

  5

Total

30

Solution 7
(i)    By observation of digits after decimal point the following table is constructed
            
        

Digit

Frequency

0

2

1

5

2

5

3

8

4

4

5

5

6

4

7

4

8

5

9

8

Total

50


                                                                                                  
(ii)    From the above table the least frequency is 2 of digit 0, and the maximum frequency is 8 of digit 3 and 9. So, the most frequently occurring digits are 3 and 9 and the least occurring digit is 0.
                                                                                                          

Solution 8
(i) Class intervals will be 0 - 5, 5 - 10, 10 -15.....
    The grouped frequency distribution table is as follows:
    
                       

Hours

Number of children

0 - 5

10

5 - 10

13

10 - 15

 5

15 - 20

 2

Total

30

                                                                                         
(ii) The number of children, who watched TV for 15 or more hours a week
        is 2 (i.e. number of children in class interval 15 - 20).

Solution 9
To construct a grouped frequency table of class size 0.5 and starting from class interval 2 - 2.5.  So, our class intervals will be as 2 - 2.5, 2.5 - 3, 3 - 3.5.......  Required grouped frequency distribution table is  as below -
 

Lives of batteries (in hours)

Number of batteries

2 - 2.5

  2

2.5 - 3.0

  6

3.0 - 3.5

14

3.5 - 4.0

11

4.0 - 4.5

  4

4.5 - 5.0

  3

Total

40

Chapter 14 - Statistics Exercise Ex. 14.3

Solution 1
(i) By representing causes on x axis and family fatality rate on y axis and choosing an appropriate scale (1 unit = 5% for y axis) we can draw the graph of information given above, as following

      Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics    

All the rectangle bars are of same width and having equal spacing between them.

(ii) Reproductive health condition is the major cause of women's ill health and death worldwide as 31.8% of women are affected by it.      

Solution 2
(i).    By representing section (variable) on x axis and number of girls per thousand boys on y axis we can draw the graph of information given as above and choosing an appropriate scale (1 unit = 100 girls for y axis)

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

Here all the rectangle bars are of same width and have equal spacing in between them.

Solution 3
(i).    By taking polling results on x axis and seats won as y axis and choosing an appropriate scale (1 unit = 10 seats for y axis) we can draw the required graph of above information as below -

       Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

    Here rectangle bars are of same width  and have equal spacing in between them.  

(ii).    We may find that political party 'A' won maximum number of seats.

Solution 4
(i).    Length of leaves are represented in a discontinuous class intervals having a difference of 1 in between them. So we have to add   to each upper class limit and also have to subtract 0.5 from the lower class limits so as to make our class intervals continuous.
    

Length (in mm)

Number of leaves

117.5 - 126.5

3

126.5 - 135.5

5

135.5 - 144.5

9

144.5 - 153.5

12

153.5 - 162.5

5

162.5 - 171.5

4

171.5 - 180.5

2



Now taking length of leaves on x axis and number of leaves on y axis we can draw the histogram of this information as below -
 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

Here 1 unit on y axis represents 2 leaves.    

(ii).    Other suitable graphical representation of this data could be frequency polygon.  

(iii).    No as maximum number of leaves (i.e. 12) have their length in between of 144.5 mm and 153.5 mm. It is not necessary that all have their lengths as 153 mm.

Solution 5
(i).    By taking life time (in hours) of neon lamps on x axis and number of lamps on y axis we can draw the histogram of the given information as below -
 
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 
Here 1 unit on y axis represents 10 lamps.

(ii).    Number of neon lamps having their lifetime more than 700 are sum of number of neon lamps having their lifetime as   700 - 800, 800 - 900, and 900 - 1000.
So number of neon lamps having their lifetime more than 700 hours is 184. (74 + 62 + 48 = 184)

Solution 6
We can find class marks of given class intervals by using formula -

Class mark  Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 
 
 

Section A

Section B

Marks

Class marks

Frequency

Marks

Class marks

Frequency

0 - 10

5

3

0 - 10

5

5

10 - 20

15

9

10 - 20

15

19

20 - 30

25

17

20 - 30

25

15

30 - 40

35

12

30 - 40

35

10

40 - 50

45

9

40 - 50

45

1

 
Now taking class marks on x axis and frequency on y axis and choosing an appropriate scale (1 unit = 3 for y axis) we can draw frequency polygon as below -

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

From the graph we can see performance of students of section 'A' is better than the students of section 'B' as for good marks.  

Solution 7
We observe that given data is not having its class intervals continuous. There is a gap of 1 in between of them. So we have to add Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics = 0.5  to upper class limits and subtract 0.5 from
lower class limits.
Also class mark of each interval can be found by using formula -
 
Class mark  Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 

 
Now continuous data with class mark of each class interval can be represented as following -
 

Number of balls

Class mark

Team A

Team B

0.5 - 6.5

3.5

2

5

6.5 - 12.5

9.5

1

6

12.5 - 18.5

15.5

8

2

18.5 - 24.5

21.5

9

10

24.5 - 30.5

27.5

4

5

30.5 - 36.5

33.5

5

6

36.5 - 42.5

39.5

6

3

42.5 - 48.5

45.5

10

4

48.5 - 54.5

51.5

6

8

54.5 - 60.5

57.5

2

10



Now by taking class marks on x axis and runs scored on y axis we can construct frequency polygon as following -
 
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
Solution 8
Here data is having class intervals of varying width. We may find proportion of children per 1 year interval as following -
   

Age (in years)

Frequency (Number of children)

Width of class

Length of rectangle

1 - 2

 

5

 

1

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

2 - 3

3

1

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

3 - 5

6

2

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

5 - 7

12

2

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

7 - 10

9

3

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

10 - 15

10

5

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

15 - 17

4

2

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics



Now taking age of children on x axis and proportion of children per 1 year interval on y axis we may draw histogram as below -
 
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 

Solution 9
(i).    Given data is having class intervals of varying width. We need to compute the adjusted frequency

Number of letters

Frequency (Number of surnames)

Width of class

Length of rectangle

1 - 4

6

3

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

4 - 6

30

2

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

6 - 8

44

2

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

8 -12

16

4

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

12 - 20

4

8

Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics 

                            

Now by taking number of letters on x axis and proportion of number of surnames per 2 letters interval on y axis and choosing an appropriate scale (1 unit = 4 students for y axis) we will construct the histogram as below

 
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

(ii).    The class interval in which the maximum number of surname lie is
6 - 8 as there are  44 number of surnames in it i.e. maximum for this data.  

Chapter 14 - Statistics Exercise Ex. 14.4

Solution 1
The number of goals scored by team is
2, 3, 4, 5, 0, 1, 3, 3, 4, 3
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 
Arranging the number of goals in ascending order
0, 1, 2, 3, 3, 3, 3, 4, 4, 5
As the number of observations is 10. 10 is an even number. So, median score will be
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

Mode of data is the observation with the maximum frequency in data.
So, mode score of data is 3 as it is having maximum frequency as 4 in the data.  

Solution 2
The marks of 15 students in mathematics test are
    41, 39, 48, 52, 46, 62, 54, 40, 96, 52, 98, 40, 42, 52, 60
 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 
 
Arranging the scores obtained by 15 students in an ascending order
    39, 40, 40, 41, 42, 46, 48, 52, 52, 52, 54, 60, 62, 96, 98
As the number of observations is 15 that is odd so, median of data will be Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics = 8th observation while data is arranged in an ascending or descending order
So, median score of data = 52   
Mode of data is the observation with the maximum frequency in data. So mode of this data is 52 having the highest frequency in data as 3.

Solution 3
Total number of observation in the given data is 10 (even number). So median of this data will be mean of Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics  i.e. 5th and Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics  i.e. 6th observations
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
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.  

Solution 5
As
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 
 Valaues of Ncert Solutions Cbse Class 9 Mathematics Chapter - Statisticsand Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics can be computed
 

Salary (in Rs) (xi)

Number of workers (fi)

fixi

3000

16

3000 * 16 = 48000

4000

12

4000 * 12 = 48000

5000

10

5000 * 10 = 50000

6000

8

6000 *  8 = 48000

7000

6

7000 *  6 = 42000

8000

4

8000 *  4 = 32000

9000

3

9000 *  3 = 27000

10000

1

10000 * 1 = 10000

Total

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

 Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics

 
Ncert Solutions Cbse Class 9 Mathematics Chapter - Statistics
 
So, mean salary of 60 workers is Rs 5083.33.
Solution 6
(i) Mean is appropriate measure of central tendency in all the cases where it is important to take all observations into account and data does not have any extreme values for example in case of temperature of a month
(ii) Mean is not suitable in cases where there are very high and low values for example salary in a company.