Statistics (Exercise 14E) RD Sharma Solutions | Mathematics (Maths) Class 10 PDF Download

 Page 1


 
30. Find the median of the following data b
Marks 0 -
10
10 -
20
20 -
30
30 -
40
40 -
50
50 -
60
60 -
70
70 -
80
80 -
90
90 -
100
Number of 
Students
5 3 4 3 3 4 7 9 7 8
Sol: 
The frequency distribution table of less than type is given as follows:
Marks (upper class limits) Cumulative frequency (cf)
Less than 10 5
Less than 20 5 + 3 = 8
Less than 30 8 + 4 = 12
Less than 40 12 + 3 = 15
Less than 50 15 + 3 = 18
Less than 60 18 + 4 = 22
Less than 70 22 + 7 = 29
Less than 80 29 + 9 = 38
Less than 90 38 + 7 = 45
Less than 100 45 + 8 = 53
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
Here, N = 53 = 26.5.
Mark the point A whose ordinate is 26.5 and 
its x-coordinate is 66.4.
Page 2


 
30. Find the median of the following data b
Marks 0 -
10
10 -
20
20 -
30
30 -
40
40 -
50
50 -
60
60 -
70
70 -
80
80 -
90
90 -
100
Number of 
Students
5 3 4 3 3 4 7 9 7 8
Sol: 
The frequency distribution table of less than type is given as follows:
Marks (upper class limits) Cumulative frequency (cf)
Less than 10 5
Less than 20 5 + 3 = 8
Less than 30 8 + 4 = 12
Less than 40 12 + 3 = 15
Less than 50 15 + 3 = 18
Less than 60 18 + 4 = 22
Less than 70 22 + 7 = 29
Less than 80 29 + 9 = 38
Less than 90 38 + 7 = 45
Less than 100 45 + 8 = 53
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
Here, N = 53 = 26.5.
Mark the point A whose ordinate is 26.5 and 
its x-coordinate is 66.4.
 
Thus, median of the data is 66.4.
31. The given distribution shows the number of wickets taken by the bowlers in one-day 
international cricket matches:
Number of 
Wickets
Less 
than
15
Less 
than
30
Less 
than
45
Less 
than
60
Less 
than
75
Less 
than
90
Less 
than
105
Less 
than
120
Number of 
bowlers
2 5 9 17 39 54 70 80
Sol: 
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
Page 3


 
30. Find the median of the following data b
Marks 0 -
10
10 -
20
20 -
30
30 -
40
40 -
50
50 -
60
60 -
70
70 -
80
80 -
90
90 -
100
Number of 
Students
5 3 4 3 3 4 7 9 7 8
Sol: 
The frequency distribution table of less than type is given as follows:
Marks (upper class limits) Cumulative frequency (cf)
Less than 10 5
Less than 20 5 + 3 = 8
Less than 30 8 + 4 = 12
Less than 40 12 + 3 = 15
Less than 50 15 + 3 = 18
Less than 60 18 + 4 = 22
Less than 70 22 + 7 = 29
Less than 80 29 + 9 = 38
Less than 90 38 + 7 = 45
Less than 100 45 + 8 = 53
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
Here, N = 53 = 26.5.
Mark the point A whose ordinate is 26.5 and 
its x-coordinate is 66.4.
 
Thus, median of the data is 66.4.
31. The given distribution shows the number of wickets taken by the bowlers in one-day 
international cricket matches:
Number of 
Wickets
Less 
than
15
Less 
than
30
Less 
than
45
Less 
than
60
Less 
than
75
Less 
than
90
Less 
than
105
Less 
than
120
Number of 
bowlers
2 5 9 17 39 54 70 80
Sol: 
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
 
Here, N = 80 = 40.
Mark the point A whose ordinate is 40 and 
its x-coordinate is 76.
Thus, median of the data is 76.
32.
Marks 0 10 10 20 20 30 30 - 40 40 50 50 60 60 70 70 80
No of 
Students
4 6 10 10 25 22 18 5
Sol: 
The frequency distribution table of more than type is as follows:
Marks (upper class limits) Cumulative frequency (cf)
More than 0 96 + 4 = 100
More than 10 90 + 6 = 96
More than 20 80 + 10 = 90
More than 30 70 + 10 = 80
More than 40 45 + 25 = 70
More than 50 23 + 22 = 45
More than 60 18 + 5 = 23
More than 70 5
Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis,
its ogive can be drawn as follows:  
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30. Find the median of the following data b
Marks 0 -
10
10 -
20
20 -
30
30 -
40
40 -
50
50 -
60
60 -
70
70 -
80
80 -
90
90 -
100
Number of 
Students
5 3 4 3 3 4 7 9 7 8
Sol: 
The frequency distribution table of less than type is given as follows:
Marks (upper class limits) Cumulative frequency (cf)
Less than 10 5
Less than 20 5 + 3 = 8
Less than 30 8 + 4 = 12
Less than 40 12 + 3 = 15
Less than 50 15 + 3 = 18
Less than 60 18 + 4 = 22
Less than 70 22 + 7 = 29
Less than 80 29 + 9 = 38
Less than 90 38 + 7 = 45
Less than 100 45 + 8 = 53
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
Here, N = 53 = 26.5.
Mark the point A whose ordinate is 26.5 and 
its x-coordinate is 66.4.
 
Thus, median of the data is 66.4.
31. The given distribution shows the number of wickets taken by the bowlers in one-day 
international cricket matches:
Number of 
Wickets
Less 
than
15
Less 
than
30
Less 
than
45
Less 
than
60
Less 
than
75
Less 
than
90
Less 
than
105
Less 
than
120
Number of 
bowlers
2 5 9 17 39 54 70 80
Sol: 
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
 
Here, N = 80 = 40.
Mark the point A whose ordinate is 40 and 
its x-coordinate is 76.
Thus, median of the data is 76.
32.
Marks 0 10 10 20 20 30 30 - 40 40 50 50 60 60 70 70 80
No of 
Students
4 6 10 10 25 22 18 5
Sol: 
The frequency distribution table of more than type is as follows:
Marks (upper class limits) Cumulative frequency (cf)
More than 0 96 + 4 = 100
More than 10 90 + 6 = 96
More than 20 80 + 10 = 90
More than 30 70 + 10 = 80
More than 40 45 + 25 = 70
More than 50 23 + 22 = 45
More than 60 18 + 5 = 23
More than 70 5
Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis,
its ogive can be drawn as follows:  
 
33. The heights of 50 girls of Class X of a school are recorded as follows:
Height
(in cm)
135 - 140 140 145 145 150 150 155 155 160 160 165
No of 
Students
5 8 9 12 14 2
for the above data.
Sol: 
The frequency distribution table of more than type is as follows:
Height (in cm) (lower class limit) Cumulative frequency (cf)
More than 135 5 + 45 = 50
More than 140 8 + 37 = 45
More than 145 9 + 28 = 37
More than 150 12 + 16 = 28
More than 155 14 + 2 = 16
More than 160 2
Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis,
its ogive can be drawn as follows:  
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30. Find the median of the following data b
Marks 0 -
10
10 -
20
20 -
30
30 -
40
40 -
50
50 -
60
60 -
70
70 -
80
80 -
90
90 -
100
Number of 
Students
5 3 4 3 3 4 7 9 7 8
Sol: 
The frequency distribution table of less than type is given as follows:
Marks (upper class limits) Cumulative frequency (cf)
Less than 10 5
Less than 20 5 + 3 = 8
Less than 30 8 + 4 = 12
Less than 40 12 + 3 = 15
Less than 50 15 + 3 = 18
Less than 60 18 + 4 = 22
Less than 70 22 + 7 = 29
Less than 80 29 + 9 = 38
Less than 90 38 + 7 = 45
Less than 100 45 + 8 = 53
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
Here, N = 53 = 26.5.
Mark the point A whose ordinate is 26.5 and 
its x-coordinate is 66.4.
 
Thus, median of the data is 66.4.
31. The given distribution shows the number of wickets taken by the bowlers in one-day 
international cricket matches:
Number of 
Wickets
Less 
than
15
Less 
than
30
Less 
than
45
Less 
than
60
Less 
than
75
Less 
than
90
Less 
than
105
Less 
than
120
Number of 
bowlers
2 5 9 17 39 54 70 80
Sol: 
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-
axis, its ogive can be drawn as follows:
 
Here, N = 80 = 40.
Mark the point A whose ordinate is 40 and 
its x-coordinate is 76.
Thus, median of the data is 76.
32.
Marks 0 10 10 20 20 30 30 - 40 40 50 50 60 60 70 70 80
No of 
Students
4 6 10 10 25 22 18 5
Sol: 
The frequency distribution table of more than type is as follows:
Marks (upper class limits) Cumulative frequency (cf)
More than 0 96 + 4 = 100
More than 10 90 + 6 = 96
More than 20 80 + 10 = 90
More than 30 70 + 10 = 80
More than 40 45 + 25 = 70
More than 50 23 + 22 = 45
More than 60 18 + 5 = 23
More than 70 5
Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis,
its ogive can be drawn as follows:  
 
33. The heights of 50 girls of Class X of a school are recorded as follows:
Height
(in cm)
135 - 140 140 145 145 150 150 155 155 160 160 165
No of 
Students
5 8 9 12 14 2
for the above data.
Sol: 
The frequency distribution table of more than type is as follows:
Height (in cm) (lower class limit) Cumulative frequency (cf)
More than 135 5 + 45 = 50
More than 140 8 + 37 = 45
More than 145 9 + 28 = 37
More than 150 12 + 16 = 28
More than 155 14 + 2 = 16
More than 160 2
Taking lower class limits of on x-axis and their respective cumulative frequencies on y-axis,
its ogive can be drawn as follows:  
 
34. The monthly consumption of electricity (in units) of some families of a locality is given in 
the following frequency distribution:
Monthly
Consumption
(in units)
140
160
160
180
180
200
200
220
220
240
240
260
260 -
280
Number of
Families
3 8 15 40 50 30 10
y distribution.
Sol: 
The frequency distribution table of more than type is as follows:
Height (in cm) (lower class limit) Cumulative frequency (cf)
More than 140 3 + 153 = 156
More than 160 8 + 145 = 153
More than 180 15 + 130 = 145
More than 200 40 + 90 = 130
More than 220 50 + 40 = 90
More than 240 30 + 10 = 40
More than 260 10
Taking the lower class limits of on x-axis and their respective cumulative frequencies on 
y-axis, its ogive can be drawn as follows:  
35. The following table gives the production yield per hectare of wheat of 100 farms of a 
village.
Production
Yield (kg/ha)
50 55 55 60 60 65 65- 70 70 75 75 80
Number of 
farms
2 8 12 24 238 16