Chapter 14 Statistics Ex 14.3

Question 1.
The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean and mode of the data and compare them.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 1
Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 2

Question 2.
If the median of the distribution given below is 28.5, find the values of x and y.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 3
Solution:
Given, Median = 28.5 which lies in the class (20 – 30).
Here, l = 20, f = 20, cf = 5 + x, h = 10, n = 60
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 4

Question 3.
A life insurance agent found the following data for distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to persons having age 18 years onwards but less than 60 years.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 5
Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 6
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 7

Question 4.
The lengths of 40 leaves of a plant are measured correct to nearest millimetre, and the data obtained is represented in the following table:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 8
Find the median length of the leaves.
(Hint: The data needs to be converted to continuous classes for finding the median since the formula assumes continuous classes. The classes then change to 117.5 – 126.5,126.5 -135.5,…, 171.5 -180.5.)
Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 9

Question 5.
The following table gives the distribution of the lifetime of 400 neon lamps:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 10
Find the median lifetime of a lamp.
Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 11

Question 6.
100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in the English alphabet in the surnames was obtained as follows:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 12
Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, find the modal size of the surnames.
Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 13
For mean
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 14

Question 7.
The distribution below gives the weight of 30 students of a class. Find the median weight of the students.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 15
Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics Ex 14.3 16