RBSE Solutions for Class 11 Maths Chapter 13 Measures of Dispersion Ex 13.3

Rajasthan Board RBSE Class 11 Maths Chapter 13 Measures of Dispersion Ex 13.3

Find mean and variance for the data of Q. 1. and Q.2

Question 1.

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

Solution:

Question 2.

xi	82	83	87	88	92	94	99
fi	3	2	3	2	6	3	3

Solution:

Question 3.
Find mean and standard deviation by shortcut method.

xi	70	71	72	73	74	75	76	77	78
fi	2	1	12	29	25	12	10	4	5

Solution:
Let Assumed mean A = 73
Calculation Table

In question 4 and 5, find mean and variable for frequency distribution.

Question 4.

Class	0-30	30-60	60-90	90-120	120-150	150-180	180-210
Frequency	2	3	5	10	3	5	2

Solution:
Calculation table

Question 5.

Class	0-10	10-20	20-30	30-40	40-50
Frequency	5	8	15	16	6

Solution:
Calculation table

Question 6.
Find mean, variable and standard deviation by short-cut method.

Solution:
Table to find mean, variance, standard deviation :

Question 7.
Find the mean deviation of diameter of circles in given table.

Diameter (mm)	43-46	47-50	51-54	55-58	59-62
Number of circles	15	17	21	22	25

Solution:
Here groups not continuous. To make it continuous we will subtract 0-5 from lower limit of group and add 0-5 in upper limit.
Calculation table for mean deviation and mean diameter

Thus standard deviation of given circles = 5.55 mm

Question 8.
Calculate standard deviation, its coefficient and variable coefficient of given data.

Class	0-20	20-40	40-60	60-80	80-100
Frequency	2	5	15	7	1

Solution:
Calculate Table

Question 9.
Find the mean deviation from imaginary mean 35 for following distribution.
35, 25, 33, 50, 37, 35, 33, 37, 30
Solution:

Question 10.
Find mean deviation from mean, median, and mode and coefficient of mean deviation from the following series –

Monthly Wages (in Rs.)	Number of tenants
Less than 10	3
Less than 20	8
Less than 30	16
Less than 40	26
Less than 50	37
Less than 60	50
Less than 70	56
Less than 80	60

Solution:
Cumulative frequency – 1

RBSE Solutions for Class 11 Maths