NCERT Solutions for Class 11 Maths Chapter 15 Statistics

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NCERT Solutions for Class 11 Maths Chapter 15 Statistics

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

Topics and Sub Topics in Class 11 Maths Chapter 15 Statistics:

Section Name Topic Name
15 Statistics
15.1 Introduction
15.2 Measures of Dispersion
15.3 Range
15.4 Mean Deviation
15.5 Variance and Standard Deviation
15 .6 Analysis of Frequency Distributions

NCERT Solutions for Class 11 Maths Statistics Ex 15.1

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

Ex 15.1 Class 11 Maths 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 Q1

Ex 15.1 Class 11 Maths 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 Q2

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q2.1

Ex 15.1 Class 11 Maths 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 Q3

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q3.1

Ex 15.1 Class 11 Maths 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 Q4

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

Ex 15.1 Class 11 Maths Question 5.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q5
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q5.1

Ex 15.1 Class 11 Maths Question 6.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q6
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q6.1

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

Ex 15.1 Class 11 Maths Question 7.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q7
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q7.1

Ex 15.1 Class 11 Maths Question 8.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q8
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q8.1

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

Ex 15.1 Class 11 Maths Question 9.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q9
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q9.1

Ex 15.1 Class 11 Maths Question 10.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q10
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q10.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q10.2

Ex 15.1 Class 11 Maths Question 11.
Find the mean deviation about median for the following data:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q11
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q11.1

Ex 15.1 Class 11 Maths 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 Q12
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.1 Q12.1
[Hint: Convert the given data into continuous frequency distribution by subtracting 0.5 from 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 Q12.2

NCERT Solutions for Class 11 Maths Chapter 15 Statistics (सांख्यिकी) Hindi Medium Ex 15.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics (सांख्यिकी)
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Exercise 15.1 in Hindi Medium
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Exercise 15.1
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1 in pdf form
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1 free download
NCERT Solutions for Class 11 Maths Chapter 15 Exercise 15.1 all question answers
11 Maths Exercise 15.1 solutions in hindi
11 Maths Exercise 15.1 solutions in pdf
11 Maths Exercise 15.1 solutions free download
11 Maths Exercise 15.1 solutions all question guide

NCERT Solutions for Class 11 Maths Statistics Ex 15.2

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

Ex 15.2 Class 11 Maths 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 Q1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q1.1

Ex 15.2 Class 11 Maths 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 Q2

Ex 15.2 Class 11 Maths 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
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q3

Ex 15.2 Class 11 Maths Question 4.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q4
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q4.1

Ex 15.2 Class 11 Maths Question 5.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q5
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q5.1

Ex 15.2 Class 11 Maths Question 6.
Find the mean and standard deviation using short-cut method
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q6
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q6.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q6.2

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

Ex 15.2 Class 11 Maths Question 7.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q7
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q7.1

Ex 15.2 Class 11 Maths Question 8.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q8
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q8.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q8.2

Ex 15.2 Class 11 Maths Question 9.
Find the mean, variance and standard deviation using short-cut method.
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q9
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q9.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.2 Q9.2

Ex 15.2 Class 11 Maths 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 Q10
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 Q10.1

NCERT Solutions for Class 11 Maths Statistics Ex 15.3

Ex 15.3 Class 11 Maths Question 1.
From the data given below state which group is more variable, A or B?
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1
Solution:
For Group A :
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1.2

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q1.3

Ex 15.3 Class 11 Maths Question 2.
From the prices of shares X and Y below, find out which is more stable in value:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q2
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q2.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q2.2

Ex 15.3 Class 11 Maths Question 3.
An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q3
(i) Which firm A or B pays larger amount as monthly wages?
(ii) Which firm, AorB, shows greater variability in individual wages?
Solution:
(i) Firm A :
Number of wage earners (n1) = 586
Mean of monthly wages (\(\overline { { x }_{ 1 } } \)) = Rs.5253
∴ Total monthly wages = 5253 x 586
= Rs. 3078258
Firm B :
Number of wage earners (n2) = 648
Mean of monthly wages (\(\overline { { x }_{ 2 } } \)) = Rs.5253
∴ Total monthly wages = 5253 x 648
= Rs. 3403944
Hence, Firm B pays larger amount as monthly wages.

(ii) Since both the firms have same mean of monthly wages, so the firm with greater variance will have more variability in individual wages. Thus firm B will have more variability in individual wages.

Ex 15.3 Class 11 Maths Question 4.
The following is the record of goals scored by team A in a football session:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q4
For the team B, mean number of goals scored per match was 2 with a standard deviation 1.25 goals. Find which team may be considered more consistent?
Solution:
For team A:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q4.1

Ex 15.3 Class 11 Maths Question 5.
The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of 50 plant products are given below:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q5
Which is more varying, the length or weight?
Solution:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q5.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Ex 15.3 Q5.2

Class 11 Maths NCERT Solutions  – Miscellaneous Questions

Miscellaneous Exercise Class 11 Maths Question 1:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q1

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q1.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q1.2

Ex 15.3 Class 11 Maths Question 2:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q2

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q2.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q2.2

Ex 15.3 Class 11 Maths Question 3:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q3

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q3.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q3.2

Ex 15.3 Class 11 Maths Question 4:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q4

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q4.1

Ex 15.3 Class 11 Maths Question 5:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q5

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q5.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q5.2

Ex 15.3 Class 11 Maths Question 6:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q6

Ans:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q6.1

Ex 15.3 Class 11 Maths Question 7:

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q7
Ans:
NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q7.1

NCERT Solutions for Class 11 Maths Chapter 15 Statistics Miscellaneous Ex Q7.2

Exercise 15.1

Q1. Calculate the mean deviation about the mean for the given data

5, 8, 9, 10, 11, 13, 14, 18

Q2Calculate the mean deviation about the mean for the given data

39, 71, 49, 41, 43, 56, 64, 47, 55, 45

Q3. Calculate the mean deviation about the median for the given data:

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

Q4. Calculate the mean deviation about the median for the given data:

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

Q5. Calculate the mean deviation about the mean for the given data

xi 5 10 15 20 25
fi 7 4 6 3 5

Q6. Calculate the mean deviation about the mean for the given data

xi 10 10 15 20 25
fi 7 4 6 3 5

Q7. Calculate the mean deviation about the median for the given data

xi 10 10 15 20 25
fi 7 4 6 3 5
xi 5 7 9 10 12 15
fi 8 6 2 2 2 6

Q8. Calculate the mean deviation about the median for the given data

xi 15 21 27 30 35
fi 3 5 6 7 8

Q9. Calculate the mean deviation about the mean for the given data:

Income per day Number of persons
0 – 100 4
100 – 200 8
200 – 300 9
300 – 400 10
400 – 500 7
500 – 600 5
600 – 700 4
700 – 800 3

Q10. Calculate the mean deviation about the mean for the given data:

Height in cm Number of boys
95 – 105 9
105 – 115 13
115 – 125 26
125 – 135 30
135 – 145 12
145 – 155 10

Q11. Calculate the mean deviation about the median for the given data:

Marks Number of girls
0 – 10 6
10 – 20 8
20 – 30 14
30 – 40 16
40 – 50 4
50 – 60 2

Q12.  Calculate the mean deviation about the median for the given data:

Age Number
16 – 20 5
21 – 25 6
26 – 30 12
31 – 35 14
36 – 40 26
41 – 45 12
46 – 50 16
51 – 55 9

Exercise 15.2

Q1. Calculate mean and variance for the given data 6, 7, 10, 12, 13, 4, 8, 12

Q2. Calculate the mean and variance for the first n natural numbers.

Q3. Calculate the mean and variance for the first 10 multiples of 3.

Q4. Calculate the mean and variance for the data

xi 6 10 14 18 24 28 30
fi 2 4 7 12 8 4 3

Q5. Calculate the mean and variance for the data

xi 92 93 97 98 102 104 109
fi 3 2 3 2 6 3 3

Q6. Calculate the mean and standard deviation using short-cut method.

xi 60 61 62 63 64 65 66 67 68
fi 2 1 12 29 25 12 10 4 5

Q7. Calculate the mean and variance for the given frequency distribution.

Classes 0 – 30 30 – 60 60 – 90 90 – 120 120 – 150 150 – 180 180 – 210
Frequencies 2 3 5 10 3 5 2

Q8. Calculate the mean and variance for the following frequency distribution.

Classes 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Frequencies 5 8 15 16 6

Q9. Calculate the mean, variance and standard deviation using short – cut method:

Height in cm Number of children
70 – 75 3
75 – 80 4
80 – 85 7
85 – 90 7
90 – 95 15
95 – 100 9
100 – 105 6
105 – 110 6
110 – 115 3

Q10. The diameters of circles (in mm) drawn in a design are given below:

Diameters Number of Children
33 – 36 15
37 – 40 17
41 – 44 21
45 – 48 22
49 – 52 25

Exercise 15.3

Q1. From the data given below state which group is more variable, A or B 

Marks 10 – 20 20 – 30 30 – 40 40 – 50 50 – 60 60 – 70 70 – 80
Group A 9 17 32 33 40 10 9
Group B 10 20 30 25 43 15 7

Q2. From the prices of shares X and Y below, find out which is more stable in value.

X 35 54 52 53 56 58 52 50 51 49
Y 108 107 105 105 106 107 104 103 104 101

Q3. An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results:

  Firm A Firm B
No. of wage earners 586 648
Mean of monthly wages Rs. 5253 Rs. 5253
Variance of the distribution of wages 100 121

(i) Which firm A or B pays larger amount as monthly wages?

(ii) Which firm, A or B, shows greater variability in individual wages?

Q4. The following is the record of goals scored by team A in a football session:

Number of goals scored 0 1 2 3 4
Number of matches 1 9 7 5 3

For team B, the mean number of goals scored per match was 2 with a standard deviation of 1.25 goals. Find which team may be considered more consistent?