CLASS 10 MATH NCERT SOLUTIONS FOR CHAPTER – 14 Statistics Ex – 14.1

Statistics

Question 1.
A survey was conducted by a group of students as a part of their environmental 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 Solutions for Class 10 Maths Chapter 14 Statistics 1

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

Solution:
Let us find the mean of the data by the direct method.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 2
Hence, we have used the direct method to find the mean of the given data, because the numerical values of f1 and x1 are small.

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

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 3

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

Solution:
In this case, we can use step-deviation method because the sata is large.
Here, a = 150 and h = 20
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 4

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 Solutions for Class 10 Maths Chapter 14 Statistics 5

Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 6

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

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 7

Solution:
Let us find the mean of the data by the direct method.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 8

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 Solutions for Class 10 Maths Chapter 14 Statistics 9

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

Solution:
Let us find the mean number of mangoes by the direct method.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 10
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 11
We have used the direct method to find the mean number of mangoes because the values of f1 and x1 are small.

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

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 12

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

Solution:
Here, a = 225 and h = 50
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 13
Hence, the  mean daily ecpenditure on food is ₹ 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:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 14

Find the mean concentration of SO2 in the air.

Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 15
Hence, the mean concentration of SO2 in air is 0.099 ppm.

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 Solutions for Class 10 Maths Chapter 14 Statistics 16

Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 17

Ex 14.1 Class 10 Maths Question 9.
The following table gives the literacy rate (in percentage) of 35 cities. Find the mean literacy rate.

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 18

Solution:
Here, h = 10
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 19
Hence, the mean literacy rate is 69.43%.