Class 11 Maths NCERT Solutions Chapter 15 - Statistics

Class 11 Maths NCERT Solutions 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

Question 2.
38, 70, 48, 40, 42, 55, 63, 46, 54, 44
Solution:
Mean of the given data is

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

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

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

Question 5.

Solution:

Question 6.

Solution:

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

Question 7.

Solution:

Question 8.

Solution:

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

Question 9.

Solution:

Question 10.

Solution:

Question 11.
Find the mean deviation about median for the following data:

Solution:

Question 12.
Calculate the mean deviation about median age for the age distribution of 100 persons given below:

[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:

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 x_i = 6, 7, 10, 12, 13, 4, 8, 12
∴ Σx_i = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72
n = 8

Question 2.
First n natural numbers
Solution:
Here x_i = 1, 2, 3, 4, ……….n

Question 3.
First 10 multiples of 3
Solution:
Here x_i = 3, 6, 9, 12, 15, 18, 21, 27, 30,
Σx_i = 3 + 6 + 9 + 12 + 15 + 18 + 21 + 24 + 27 + 30 = 165
n = 10

Question 4.

Solution:

Question 5.

Solution:

Question 6.
Find the mean and standard deviation using short-cut method

Solution:

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

Question 7.

Solution:

Question 8.

Solution:

Question 9.
Find the mean, variance and standard deviation using short-cut method.

Solution:

Question 10.
The diameters of circles (in mm) drawn in a design are given below:

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:

Ex – 15.3

Question 1.
From the data given below state which group is more variable, A or B?

Solution:
For Group A :

Question 2.
From the prices of shares X and Y below, find out which is more stable in value:

Solution:

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:

(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 (x1¯¯¯¯¯) = Rs.5253
∴ Total monthly wages = 5253 x 586
= Rs. 3078258
Firm B :
Number of wage earners (n₂) = 648
Mean of monthly wages (x2¯¯¯¯¯) = 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.

Question 4.
The following is the record of goals scored by team A in a football session:

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:

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:

Which is more varying, the length or weight?
Solution: