# NCERT Class 10 Chapter 14 Statistics CBSE Board Sample Problems Short Answer (For CBSE, ICSE, IAS, NET, NRA 2023)

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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 - 2020 - 4040 - 6060 - 8080 - 100 1030507090 16142426x 1604201200182090x 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 - 5555 - 6060 - 6565 - 7070 - 7575 - 80 1318451662

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 ₹) 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 - 2020 - 4040 - 6060 - 8080 - 100 5812114 51325 3640

## 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 - 2020 - 4040 - 6060 - 8080 - 100 15103550 Model Class40

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 - 5050 - 6060 - 7070 - 8080 - 90 5 Modal class7

Mode = 67 given

Model class is 60 - 70

Mode

## Question

Find the unknown values in the following table:

 Class interval Frequency Cumulative Frequency 0 - 1010 - 2020 - 3030 - 4040 - 50 575 51830

### Solution

 Class interval Frequency Cumulative Frequency 0 - 1010 - 2020 - 3030 - 4040 - 50 575 51830

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

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