CLASS 10 MATH NCERT SOLUTIONS FOR CHAPTER – 14 STATISTICS EX – 14.3

Statistics

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 35

Solution:
Here h = 20.
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 36
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 38
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 39

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 40

Solution:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 41
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 42

Question 3.
A life insurance agent found the following data for the 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 43

Solution:
The given distribution is less than type and upper limits are 20, 25, 30, 35, 40, 45, 50, 55 and 60.
So, we can assume class intervals such as (15 – 20), (20 – 25), (25 – 30), (30 – 35), (35 – 40), (40 – 45), (45 – 50), (50 – 55) and (55 – 60). As the number of policy holder is in cumulative distribution. So have the frequency distribution as:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 44
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 45

Question 4.
The lengths of 40 leaves of a plant are measured correct to the nearest millimeter, and the data obtained is represented in the following table:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 46

Find the median length of the leaves.

Solution:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 47
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 48

Question 5.
The following table gives the distribution of the lifetime of 400 neon lamps:

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 49

Find the median lifetime of a lamp.

Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 50
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 51

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 52

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 53
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 54
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 55

Question 7.
The distribution below gives the weight of 30 students in a class. Find the median weight of the students.

NCERT Solutions for Class 10 Maths Chapter 14 Statistics 56

Solution:
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 57
NCERT Solutions for Class 10 Maths Chapter 14 Statistics 58

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