Chapter 15 Statistics Ex – 15.1

Find the mean deviation about the mean for the data in Exercises 1 and 2.

Question 1.

4, 7, 8, 9, 10, 12, 13, 17

Solution:

Mean of the given data is

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 1
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 2

Question 2.

38, 70, 48, 40, 42, 55, 63, 46, 54, 44

Solution:

Mean of the given data is

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 3

Question 3.

13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Solution:

Arranging the data in ascending order, we have
10, 11, 11, 12, 13, 13, 14, 16, 16, 17, 17, 18
Here n = 12 (which is even)
So median is the average of 6th and 7th observations

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 4
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 5

Question 4.

36, 72, 46, 42, 60, 45, 53, 46, 51, 49

Solution:

Arranging the data in ascending order, we have 36, 42, 45, 46, 46, 49, 51, 53, 60, 72
Here n = 10 (which is even)
So median is the average of 5th and 6th observations

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 6

Find the mean deviation about the mean for the data in Exercises 5 and 6.

Question 5.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 7

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 8

Question 6.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 9

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 10

Find the mean deviation about the median for the data in Exercises 7 and 8.

Question 7.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 11

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 25

Question 8.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 13

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 14

Find the mean deviation about the mean for the data in Exercises 9 and 10.

Question 9.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 15

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 16

Question 10.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 17

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 18
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 19

Question 11.

Find the mean deviation about median for the following data:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 20

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 21

Question 12.

Calculate the mean deviation about median age for the age distribution of 100 persons given below:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 22
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 23

[Hint: Convert the given data into continuous frequency distribution by subtracting 0.5 from the lower limit and adding 0.5 to the upper limit of each class interval]

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 24