NCERT Class 10 Chapter 14 Statistics CBSE Board Sample Problems Long Answer
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Question
The lengths of 50 leaves of a plant are measured correct to the nearest millimeter and the data obtained is represented in the following table
Length (in mm) | 109-117 | 118-126 | 127-135 | 136-144 | 145-153 | 154-162 | 163-171 |
No. of leaves | 4 | 6 | 14 | 13 | 6 | 4 | 3 |
Find the mean length of the leaves.
Solution
Class Interval | ||||
108.5-117.5 117.5-126.5 126.5-135.5 135.5-144.5 144.5-153.5 153.5-162.5 162.5-171.5 | 113 122 131 140 149 158 167 | 4 6 14 13 6 4 3 | -3 -2 -1 0 1 2 3 | -12 -12 -14 0 6 8 9 |
Total |
Given frequency distribution is not continuous. So first we have to make it continuous.
Here assumed mean (a) =140; class size =9
Now,
Hence, mean length of the leaves -137.30mm.
Question
Draw a ‘less than type’ ogive for the following frequency distribution.
Class | 15-20 | 20-25 | 25-30 | 30-35 | 35-40 | 40-45 |
Frequency | 13 | 18 | 31 | 25 | 15 | 5 |
Solution

Draw a ‘Less Than Type’ Ogive
Class | Frequency |
Less than 20 Less than 25 Less than 30 Less than 35 Less than 40 Less than 45 | 13 |
Question
In a retail market, fruit vendor were selling mangoes in packing boxes. These boxes contained varying number or mangoes. The following was the distribution.
No. of mangoes | 50-52 | 53-55 | 56-58 | 59-61 | 62-64 |
No. of boxes | 15 | 110 | 135 | 115 | 25 |
Find the mean and median number of mangoes kept in a packing box.
Solution
Class interval | Mid value () | (where a=57) | |||
49.5-52.5 52.5-55.5 55.5-58.5 58.5-61.5 61.5-64.5 | 51 54 57=a 60 63 | -2 -1 0 1 2 | 15 110 135 115 25 | -30 -110 0 115 50 | 15 125 260 375 400 |
Mean
For median: Median
Here
Median class is 55.5-58.5
Median
Question
The following table gives production yield of rice per hectare in some farms of a village:
Production yield (in kg/hectare) | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 |
No. of farms | 3 | 9 | 12 | 20 | 6 |
Draw a more than type’ ogive. Also, find median from the curve.
Solution
Production yield (in kg/hectare) Class interval | Frequency | Production yield more than or eual to | |
10-20 20-30 30-40 40-50 50-60 | 3 9 12 20 6 | 10 20 30 40 50 | 50 47 38 26 6 |

Frequency
Question
Life time (in hours) | More than or equal to 240 | More than or equal to 280 | More than or equal to 320 | More than or equal to 360 | More than or equal to 400 | More than or equal to 440 | More than or equal to 480 |
Number of bulbs | 100 | 95 | 87 | 77 | 47 | 22 | 10 |
Draw a more than type ogive and from it find median. Verify it by actual calculations.
Solution
More than or equal to | Number of bulbs |
240 280 320 360 400 440 480 | 100 95 87 77 47 22 10 |

Draw a More Than Type Ogive and from It Find Median
Median from curve is 396.
Class interval | Frequency | Cumulative frequency | |
240-280 280-320 320-360 360-400 400-440 440-480 480-520 | 5 8 10 30 25 12 10 | 5 13 23 53 78 90 100 | Median class |
100 |
Median
Question
Change the following distribution to a ‘more than type’ distribution. Hence draw the ‘more than type’ ogive for this distribution.
Class Interval | 20-30 | 30-40 | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
Frequency | 10 | 8 | 12 | 24 | 6 | 25 | 15 |
Solution
Class Interval | Cumulative Frequency |
More than or equal to 20 | 100 |
More than or equal to 30 | 90 |
More than or equal to 40 | 82 |
More than or equal to 50 | 70 |
More than or equal to 60 | 46 |
More than or equal to 70 | 40 |
More than or equal to 80 | 15 |
Plot of points (20. 100), (30. 90), (40, 82), (50. 70), (60,46), (70. 40) and (80. 15)
Join the points to get a curve
Question
The mean of the following distribution is 18. Find the frequency f of the class 19 —21.
Class | 11-13 | 13-15 | 15-17 | 17-19 | 19-21 | 21-23 | 23-25 |
Frequency | 3 | 6 | 9 | 13 | f | 5 | 4 |
Solution
Class | x | f | |
11-13 | 12 | 3 | 36 |
13-15 | 14 | 6 | 84 |
15-17 | 16 | 9 | 144 |
17-19 | 18 | 13 | 234 |
19-21 | 20 | f | 20f |
21-23 | 22 | 5 | 110 |
23-25 | 24 | 4 | 96 |
Mean
Question
If the median of the following frequency distribution is 32.5. Find the values of and .
Class | 0-10 | 10-20 | 20-30 | 30-40 | 40-50 | 50-60 | 70-80 | Total |
Frequency | 5 | 9 | 12 | 3 | 2 | 40 |
Solution
Class | Frequency | Cumulative Frequency |
0-10 | ||
10-20 | 5 | |
20-30 | 9 | |
30-40 | 12 | |
40-50 | ||
50-60 | 3 | |
60-70 | 2 | |
40 |
Median median class is 30-40.
Now
Also,
Question
The following distribution gives the daily income of 50 workers of a factory
Daily Income | 400-420 | 400-420 | 400-420 | 400-420 | 400-420 |
Number of workers | 12 | 12 | 12 | 12 | 12 |
Convert this distribution to less than a type of cumulative frequency distribution and draw its ogive.
Solution
Daily Income | Number of workers | Cumulative Frequency |
400-420 | 12 | 12 |
420-440 | 14 | 26 |
440-460 | 8 | 34 |
460-480 | 6 | 40 |
480-500 | 10 | 50 |
Correct Table
Drawing an ogive with coordinates
Question
Calculate Mean of the following distribution
C.I | 10-19 | 20-29 | 30-39 | 40-49 | 50-59 | 60-69 | 70-79 | 80-89 | 90-99 |
Frequency | 5 | 9 | 13 | 17 | 16 | 11 | 12 | 9 | 8 |
Solution
10-19 | 14.5 | 5 | -40 | -4 | 20 |
20-29 | 24.5 | 9 | -30 | -3 | -27 |
30-39 | 34.5 | 13 | -20 | -2 | -26 |
50-50 | 44.5 | 17 | -10 | -1 | -17 |
40-49 | 54.5 | 16 | 0 | 0 | 0 |
60-69 | 64.5 | 11 | 10 | 1 | 11 |
70-79 | 74.5 | 12 | 20 | 2 | 24 |
80-89 | 84.5 | 9 | 30 | 3 | 27 |
90-99 | 94.5 | 8 | 40 | 4 | 32 |
100 |
Question
If the mean of x and is M, find the mean of and
Solution
Mean of and is