Chapter 15 Statistics Ex – 15.2

Find the mean and variance for each of the data in Exercises 1 to 5.

Question 1.

6, 7, 10, 12, 13, 4, 8, 12

Solution:

Here xi = 6, 7, 10, 12, 13, 4, 8, 12
∴ Σxi = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72
n = 8

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 1
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 2

Question 2.

First n natural numbers

Solution:

Here xi = 1, 2, 3, 4, ……….n

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 3

Question 3.

First 10 multiples of 3

Solution:

Here xi = 3, 6, 9, 12, 15, 18, 21, 27, 30,
Σxi = 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165
n = 10

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Question 4.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 5

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 6

Question 5.

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 7

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 8

Question 6.

Find the mean and standard deviation using short-cut method

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Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 10
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 11

Find the mean and variance for the following frequency distributions in Exercises 7 and 8.

Question 7.

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Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 13

Question 8.

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Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 15
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 16

Question 9.

Find the mean, variance and standard deviation using short-cut method.

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Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 18
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 19

Question 10.

The diameters of circles (in mm) drawn in a design are given below:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 20

Calculate the standard deviation and mean diameter of the circles.

[Hint: First make the data continuous by making the classes as 32.5 – 36.5, 36.5 – 40.5, 40.5 – 44.5, 44.5 – 48.5, 48.5 – 52.5 and then proceed.]

Solution:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 21