RBSE Solutions for Class 11 Maths Chapter 13 Measures of Dispersion Ex 13.1

Rajasthan Board RBSE Class 11 Maths Chapter 13 Measures of Dispersion Ex 13.1

Question 1.
Write the formula of quartile deviation.
Solution:
Coefficient of quartile deviation

Here, Q₃ = upper quartile, Q₁ = Lower quartile.

Question 2.
For any variable series Q₁ = 61 and Q₃ = 121. Find the quartile deviation.
Solution:
Quartile deviation (Q.D.) = \(\frac { { Q }_{ 3 }-{ Q }_{ 1 } }{ 2 } \)
= \(\frac { 121-61 }{ 2 } \)
= \(\frac { 60 }{ 2 } \) = 30.

Question 3.
Find the quartile deviation and coefficient of quartile deviation of the following data.
3, 8, 11, 13, 17, 19, 20, 22, 23, 27, 31
Solution:
Given data is in assending order.
Total number of terms N = 11

Question 4.
Find the range and coefficient of range of the following table –

x	4.5	5.5	6.5	7.5	8.5	9.5	10.5	11.5
f	4	5	6	3	2	1	3	5

Solution:
Lower limit (S) = 4.5
Upper limit (L)= 11.5
Range = L – S
= 11.5 – 4.5 = 7

Thus range is 7 and coefficient of range is 0.44

Question 5.
Find the inter quartile range and its coefficient for the following series –

X	1	3	5	7
f	10	15	3	2

Solution:
We prepare a table using these datas:

X	f	c.f
1	10	10
3	15	25
5	3	28
7	2	30

Here, N = 30

Question 6.
Find the coefficient of range of the following data –

Size	10-15	15-20	20-25	25-30
Frequency	2	4	6	8

Solution:
Lower limit (S) = 10
Upper limit (L) = 30

Thus Range coefficient is 0-5.

Question 7.
Find the decile range and percentile range on the basis of following data :

X	f
0-10	3
10-20	9
20-30	8
30-40	5
40-50	7
50-60	5
60-70	7
70-80	6

Solution:

Class (x)	Frequency (f)	Cumulative frequency
0-10	3	3
10-20	9	12
20-30	8	20
30-40	5	25
40-50	7	32
50-60	5	37
60-70	7	44
70-80	6	50
	N = 50

Calculation of percentile range-

Cumulative frequency exactly greater than 45 is 50, whose corresponding class is 70 – 80

Cumulative frequency exactly greater than 5 is 12, whose corresponding class is 10-20

∴ Percentile range = 71.66 – 12.22 = 59.44
Thus Percentile range = 59.44

Question 8.
Find the decile range and percentile range of the following frequency distribution.

Marks (x)	0-10	10-20	20-30	30-40	40-50
Frequency(f)	5	8	20	14	3

Solution:

Class (x)	Frequency (f)	Cumulative frequency
0-10	5	5
10-20	8	13
20-30	20	33
30-40	14	47
40-50	3	50
	N = 30

Calculation of Decile Range –

Cumulative frequency exactly greater than 45 is 47, whose corresponding class is 30 – 40
∴ l = 30, f = 14, F = 33, h = 10

Cumulative frequency exactly greater than 5 is 13, whose corresponding class is 10 – 20
∴ l = 10, f = 8, F = 5, h = 10

Cumulative frequency exactly greater than 45 is 47, whose corresponding class is 30 – 40
∴ l = 30, f = 14, F = 33, h = 10

Cumulative frequency exactly greater than 5 is 13, whose corresponding class is 10 – 20
∴ l = 10, f = 8, F = 5, h = 10

RBSE Solutions for Class 11 Maths