NCERT Solutions for Class 11 Maths Chapter 13 Statistics Ex 13.2
Find the mean and variance for each of the data in Exercises 1 to 5.
Ex 13.2 Class 11 Maths Question 1.
6, 7, 10, 12, 13, 4, 8, 12
Solution:
Here, xi = 6, 7, 10, 12, 13, 4, 8, 12
∴ Σ xi = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72
n = 8
Ex 13.2 Class 11 Maths Question 2.
First n natural numbers
Solution:
Here, xi = 1, 2, 3, 4, ………., n
Ex 13.2 Class 11 Maths Question 3.
First 10 multiples of 3
Solution:
Here, xi = 3, 6, 9, 12, 15, 18, 21, 24, 27, 30
Σ xi = 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165
n = 10
Ex 13.2 Class 11 Maths Question 4.
xi | 6 | 10 | 14 | 18 | 24 | 28 | 30 |
fi | 2 | 4 | 7 | 12 | 8 | 4 | 3 |
Solution:
Ex 13.2 Class 11 Maths Question 5.
xi | 92 | 93 | 97 | 98 | 102 | 104 | 109 |
fi | 3 | 2 | 3 | 2 | 6 | 3 | 3 |
Solution:
Ex 13.2 Class 11 Maths Question 6.
Find 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 |
Solution:
Find the mean and variance for the following frequency distributions in Exercises 7 and 8.
Ex 13.2 Class 11 Maths Question 7.
Classes | Frequencies |
0 – 30 | 2 |
30 – 60 | 3 |
60 – 90 | 5 |
90 – 120 | 10 |
120 – 150 | 3 |
150 – 180 | 5 |
180 – 210 | 2 |
Solution:
Ex 13.2 Class 11 Maths Question 8.
Classes | Frequencies |
0 – 10 | 5 |
10 – 20 | 8 |
20 – 30 | 15 |
30 – 40 | 16 |
40 – 50 | 6 |
Solution:
Ex 13.2 Class 11 Maths Question 9.
Find the mean, variance and standard deviation using short-cut method.
Height in cms | No. 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 |
Solution:
Ex 13.2 Class 11 Maths Question 10.
The diameters of circles (in mm) drawn in a design are given below:
Diameters | No. of circles |
33 – 36 | 15 |
37 – 40 | 17 |
41 – 44 | 21 |
45 – 48 | 22 |
49 – 52 | 25 |
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:
Related Links:
NCERT Solutions for Maths Class 9
NCERT Solutions for Maths Class 10