In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 14 Statistics Ex 14.1. These solutions are based on new NCERT Syllabus.

## NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 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?

Solution:

We can calculate the mean as follows :

∴ Mean = \(\overline{x}=\frac{\sum f_{i} x_{i}}{N}=\frac{162}{20}=8.1\)

Thus, mean number of plants per house is 8.1 Since, values of x_{i} and f_{i} are small, so we have used the direct method.

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.

Solution:

Let the assumed mean, a = 150

∵ Class size, h = 20

∴ \(u_{i}=\frac{x_{i}-a}{h}=\frac{x_{i}-150}{20}\)

∴ We have the following table:

Now, \(\overline{x}\) = a + h × {\(\frac{1}{N}\) Σf_{i}u_{i}}

= 150 + 20 × \(\left(\frac{-12}{50}\right)\) = 150 – \(\frac{24}{5}\)

= 150 – 4.8 = 145.20

Question 3.

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

Solution:

Let the assumed mean, a = 18

∵ Class size, h = 2

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-18}{2}\)

Now, we have the following table:

⇒ [f + 44] (0) = 2[f – 20]

⇒ 2[f – 20] = 0 ⇒ f = 20

Thus, missing frequency is 20.

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.

Solution:

Let the assumed mean, a = 75.5

∵ Class size, h = 3

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-75.5}{3}\)

Now, we have the following table:

Thus, the mean heart beats per minute is 75.9.

Question 5.

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

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

Solution:

Let the assumed mean, a = 57

∴ d_{i} = x_{i} – 57

Now, we have the following table:

Thus, the average number of mangoes per box = 57.19. We choose assumed mean method.

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.

Solution:

Let the assumed mean, a = 225

∵ Class size, (h) = 50

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-225}{50}\)

Now, we have the following table:

Thus, the mean daily expenditure on food is ₹ 211.

Question 7.

To find out the concentration of S0_{2} 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 S0_{2} in the air.

Solution:

Let the assumed mean, a = 0.14

∵ Class size, (h) = 0.04

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-0.14}{0.04}\)

Now, we have the following table:

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.

Solution:

Using the direct method, we have the following table:

Thus, mean number of days a student remained absent = 12.48.

Question 9.

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Solution:

Let the assumed mean, a = 70

∵ Class size, (h) = 10

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-70}{10}\)

Now, we have the following table:

Thus, the mean literacy rate is 69.43%

In this post, we will share NCERT Class 10th Maths Book Solutions Chapter 14 Statistics Ex 14.1. These solutions are based on new NCERT Syllabus.

## NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 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?

Solution:

We can calculate the mean as follows :

∴ Mean = \(\overline{x}=\frac{\sum f_{i} x_{i}}{N}=\frac{162}{20}=8.1\)

Thus, mean number of plants per house is 8.1 Since, values of x_{i} and f_{i} are small, so we have used the direct method.

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.

Solution:

Let the assumed mean, a = 150

∵ Class size, h = 20

∴ \(u_{i}=\frac{x_{i}-a}{h}=\frac{x_{i}-150}{20}\)

∴ We have the following table:

Now, \(\overline{x}\) = a + h × {\(\frac{1}{N}\) Σf_{i}u_{i}}

= 150 + 20 × \(\left(\frac{-12}{50}\right)\) = 150 – \(\frac{24}{5}\)

= 150 – 4.8 = 145.20

Question 3.

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

Solution:

Let the assumed mean, a = 18

∵ Class size, h = 2

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-18}{2}\)

Now, we have the following table:

⇒ [f + 44] (0) = 2[f – 20]

⇒ 2[f – 20] = 0 ⇒ f = 20

Thus, missing frequency is 20.

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.

Solution:

Let the assumed mean, a = 75.5

∵ Class size, h = 3

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-75.5}{3}\)

Now, we have the following table:

Thus, the mean heart beats per minute is 75.9.

Question 5.

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

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

Solution:

Let the assumed mean, a = 57

∴ d_{i} = x_{i} – 57

Now, we have the following table:

Thus, the average number of mangoes per box = 57.19. We choose assumed mean method.

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.

Solution:

Let the assumed mean, a = 225

∵ Class size, (h) = 50

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-225}{50}\)

Now, we have the following table:

Thus, the mean daily expenditure on food is ₹ 211.

Question 7.

To find out the concentration of S0_{2} 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 S0_{2} in the air.

Solution:

Let the assumed mean, a = 0.14

∵ Class size, (h) = 0.04

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-0.14}{0.04}\)

Now, we have the following table:

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.

Solution:

Using the direct method, we have the following table:

Thus, mean number of days a student remained absent = 12.48.

Question 9.

The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

Solution:

Let the assumed mean, a = 70

∵ Class size, (h) = 10

∴ u_{i} = \(\frac{x_{i}-a}{h}=\frac{x_{i}-70}{10}\)

Now, we have the following table:

Thus, the mean literacy rate is 69.43%