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Home Class 10th Solutions 10th Maths

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

by Sudhir
December 4, 2021
in 10th Maths, Class 10th Solutions
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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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 1
Which method did you use for finding the mean, and why?
Solution:
We can calculate the mean as follows :
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 2
∴ 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 xi and fi are small, so we have used the direct method.

Question 2.
Consider the following distribution of daily wages of 50 workers of a factory.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 3
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:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 4
Now, \(\overline{x}\) = a + h × {\(\frac{1}{N}\) Σfiui}
= 150 + 20 × \(\left(\frac{-12}{50}\right)\) = 150 – \(\frac{24}{5}\)
= 150 – 4.8 = 145.20

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 5
Solution:
Let the assumed mean, a = 18
∵ Class size, h = 2
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-18}{2}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 6
⇒ [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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 7
Solution:
Let the assumed mean, a = 75.5
∵ Class size, h = 3
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-75.5}{3}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 8
Thus, the mean heart beats per minute is 75.9.

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 9
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
∴ di = xi – 57
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 10
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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 11
Find the mean daily expenditure on food by a suitable method.
Solution:
Let the assumed mean, a = 225
∵ Class size, (h) = 50
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-225}{50}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 12
Thus, the mean daily expenditure on food is ₹ 211.

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

Question 7.
To find out the concentration of S02 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:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 13
Find the mean concentration of S02 in the air.
Solution:
Let the assumed mean, a = 0.14
∵ Class size, (h) = 0.04
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-0.14}{0.04}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 14

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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 15
Solution:
Using the direct method, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 16
Thus, mean number of days a student remained absent = 12.48.

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

Question 9.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 17
Solution:
Let the assumed mean, a = 70
∵ Class size, (h) = 10
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-70}{10}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 18

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 19
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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 1
Which method did you use for finding the mean, and why?
Solution:
We can calculate the mean as follows :
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 2
∴ 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 xi and fi are small, so we have used the direct method.

Question 2.
Consider the following distribution of daily wages of 50 workers of a factory.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 3
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:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 4
Now, \(\overline{x}\) = a + h × {\(\frac{1}{N}\) Σfiui}
= 150 + 20 × \(\left(\frac{-12}{50}\right)\) = 150 – \(\frac{24}{5}\)
= 150 – 4.8 = 145.20

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 5
Solution:
Let the assumed mean, a = 18
∵ Class size, h = 2
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-18}{2}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 6
⇒ [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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 7
Solution:
Let the assumed mean, a = 75.5
∵ Class size, h = 3
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-75.5}{3}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 8
Thus, the mean heart beats per minute is 75.9.

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 9
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
∴ di = xi – 57
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 10
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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 11
Find the mean daily expenditure on food by a suitable method.
Solution:
Let the assumed mean, a = 225
∵ Class size, (h) = 50
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-225}{50}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 12
Thus, the mean daily expenditure on food is ₹ 211.

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

Question 7.
To find out the concentration of S02 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:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 13
Find the mean concentration of S02 in the air.
Solution:
Let the assumed mean, a = 0.14
∵ Class size, (h) = 0.04
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-0.14}{0.04}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 14

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.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 15
Solution:
Using the direct method, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 16
Thus, mean number of days a student remained absent = 12.48.

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1

Question 9.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 17
Solution:
Let the assumed mean, a = 70
∵ Class size, (h) = 10
∴ ui = \(\frac{x_{i}-a}{h}=\frac{x_{i}-70}{10}\)
Now, we have the following table:
NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 18

NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.1 19
Thus, the mean literacy rate is 69.43%

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NCERT Class 10th Maths Solutions Chapter 14 Statistics Ex 14.2

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