Class X

Statistics EXERCISE : 14.1

Question 1. A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality. Find the mean number of plants per house.

Which method did you use for finding the mean, and why?

Sol. We can calculate the mean as:

Thus, mean number of plants per house is 8.1.

Since, values of x_i and f_i are small

We have used the direct method.

Class X Statistics EXERCISE : 14.1

Question 2. Consider the following distribution of daily wages of 50 workers of a factory.

Find the mean daily wages of the workers of the factory by using an appropriate method.

Sol. Let the assumed mean, a = 150

Class interval h = 20

We have the following table:

Now

= 145.2

Class X Statistics EXERCISE : 14.1

Question 3. The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs. 18. Find the missing frequency f.

Sol. Let the assumed mean, a = 16

Class interval h = 2

Now, we have the following table:

Since

a = 16 and h = 2

Thus, the missing frequency is 20.

Class X Statistics EXERCISE : 14.1

Question 4. Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarised as follows. Find the mean heart beats per minute for these women, choosing a suitable method.

Sol. Let the assumed mean a = 75.5

Class interval h = 3

Now, we have the following table:

Thus, the mean heart beat per minute is 75.9.

QUESTION 5. In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained carying number of mangoes. The following was the distribution of mangoes according to the number.

Find the mean number of mangoes kept in a packing box. Which of finding the mean did you choose?

Sol. Let the assumed mean a = 60

Here, class interval h = 3

Now, we have the following table:

= 57.19 (approx).

Thus, the average number of mangoes per box = 57.19.

QUESTION 6. The table below shows the daily expenditure on food of 25 households in a locality.

Find the mean daily expenditure on food by a suitable method.

Sol. let the assumed mean, a = 225

And class interval h = 50

We have the following table:

= 211

Thus, the mean daily expenditure of food is Rs. 211.

QUESTION 7. To find out the concentration of SO₂ in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

Find the mean concentration of SO₂ in the air.

Sol. Let the assumed mean a = 0.14

Here, class interval h = 0.04

We have the following table:

Thus, mean concentration of SO₂ in air is 0.099 ppm.

Class X Statistics EXERCISE : 14.1

QUESTION 8. A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent.