NCERT Class 10 Chapter 14 Statistics CBSE Board Sample Problems Short Answer
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Question
If the mean of the following distribution is 54, find the missing frequency X:
Class | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
Frequency | 16 | 14 | 24 | 26 | x |
Solution
Class Interval | |||
0-20 20-40 40-60 60-80 80-100 | 10 30 50 70 90 | 16 14 24 26 x | 160 420 1200 1820 90x |
Total | 80+x | 3600+90x |
Mean
Question
The following table shows the distribution of weights of 100 candidates appearing for a competition. Determine the modal weight.
Weight (in kg) | 50-55 | 55-60 | 60-65 | 65-70 | 70-75 | 75-80 |
No. of candidates | 13 | 18 | 45 | 16 | 6 | 2 |
Solution
Class Interval | |
50-55 55-60 60-65 65-70 70-75 75-80 | 13 18 45 16 6 2 |
Hear
Mode
Question
Sonic students of Class X donated for the welfare of old age persons. Their contributions are shown in the following frequency distribution:
Amount (in Rs) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 |
No. of students | 5 | 8 | 12 | 11 | 4 |
Find median and mode for their contribution.
Solution
Median
For mode modal class 40-60
Mode
Number of students | c.f. | |
0-20 20-40 40-60 60-80 80-100 | 5 8 12 11 4 | 5 13 25 36 40 |
Question
The average score of boys in the examination of a school is 71 and that of the girls is 73. The average score of the school in the examination is 71.8. Find the ratio of the number of boys to the number of girls who appeared in the examination.
Solution
Let number of boys in the school be x
Average score of boys = 71
Total score of boys in the examination of the school
Let number of girls in the school be y
Average score of girls = 73
Total score of girls in the examination of the school
Now, average score of the school in examination
Question
The following data gives the information on the observed life times (in hours) of 150 electrical components
Life time (in hours ) | 0-20 | 20-40 | 40-60 | 60-80 | 80-100 | 0-20 | 20-40 |
Frequency | 15 | 10 | 35 | 50 | 40 |
Solution
Life time (in hours ) | Frequency |
0-20 20-40 40-60 60-80 80-100 | 15 10 35 50 Model Class 40 |
Model class is 60-80
Mode
Question
Determine the missing frequency x, from the following data when Mode is 67.
Class | 40-50 | 50-60 | 60-70 | 70-80 | 80-90 |
frequency | 5 | x | 15 | 12 | 7 |
Solution
Class interval | Frequency |
40-50 50-60 60-70 70-80 80-90 | 5 Modal class 7 |
Mode =67 given
Model class is 60-70
Mode
Question
Find the unknown values in the following table:
Class interval | Frequency | Cumulative Frequency |
0-10 10-20 20-30 30-40 40-50 | 5 7 5 | 5 18 30 |
Solution
Class interval | Frequency | Cumulative Frequency |
0-10 10-20 20-30 30-40 40-50 | 5 7 5 | 5 18 30 |
From table:
Question
The mode of a distribution is 55 & the modal class is 45-60 and the frequency preceding the modal class is 5 and the frequency after the modal class is 10. Find the frequency of the modal class
Solution
Mode= 55
Modal class
Class preceding modal class
Class succeeding modal class
Mode
Question
Find the mean of 30 numbers given mean often of them is 12 and the mean of remaining 20 is 9.
Solution
Total number of mean = 30
Mean of 10 is = 12
Mean of 20 numbers is = 9
By (1) + (2)
Mean of 20 numbers =
10
Question
The mean of 5 numbers is 10. If 3 decrease each number, find the mean of the new number.
Solution
Mean of 5 nos
Since, each number is decreased by 3, then the sum is decreased by
Mean of new no
Question
The median of a data is 20. If each item is increased by 2, find the new median.
Solution
Median is the middle most item and each item is increased by 2, the new median will be
Question
The mean of 20 observations is 12. If each observation is increased by 5, then find the new mean.
Solution
If each observation is increased by 5 then the required new mean is also increased by 5.
Thus, the new mean is 17.
Question
The mean of 6, and Find the value of x
Solution
Mean
Question
Find the Mode of the following data:
Class Intervals 10 – 14 15 -19 20-24 25-29 30-34 35-39
Frequencies 30 45 75 35 25 10
Also, if the Median of the distribution is 20.8, find the Mean.
Solution
Modal class is
Mode
Using Empirical formula
3 median