Measures Of Dispersion

Question

A batsman is to be selected for a cricket team. The choice is between X and Y on the basis of their five previous scores which are:

X

Y

25

50

85

70

40

65

80

45

120

80

(a) Calculate coefficient of standard deviation, variance and coefficient of variation.

(b) Which batsman should be selected if we wants.

(i) a higher run getter, or

(ii) a more reliable batsman in the team?

Solution

(a)

Scores	Batsman x
Scores
25	–45	2025
85	+15	225
40	–30	900
80	+10	100
120	+50	2500
ΣX=350		Σx²= 570

Batsman Y

Scores		²
50	–12	144
70	8	64
65	3	9
45	–17	289
80	18	324
Σx=310		Σx²= 830

(i) Batsman X should be selected as a higher run getter as his average score (70 runs) is greater than that of Y (i.e. 62 runs)

(ii)Batsman Y is a more reliable batsman in the team because his coefficient of variance (20.77) is less than that of batsman X (c.v. 48.44)

Some More Questions From Measures of Dispersion Chapter

Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?

In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.

If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

Calculate the mean deviation about mean and standard deviation for the following distribution:

Classes

Frequencies

20–40

3

40–80

6

80–100

20

100–120

12

120–140

9

50

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Measures Of Dispersion

Some More Questions From Measures of Dispersion Chapter

Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?

In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.

If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

Calculate the mean deviation about mean and standard deviation for the following distribution:

Classes

Frequencies

20–40

3

40–80

6

80–100

20

100–120

12

120–140

9

50

A measure of dispersion is a good .supplement to the central value in understanding a frequency distribution. Comment

Define dispersion.

How many methods are there to calculate dipersion?

Define range.

Define quartile deviation.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

Classes	Frequencies
20–40	3
40–80	6
80–100	20
100–120	12
120–140	9
	50

For Daily Free Study Material Join wiredfaculty

Measures Of Dispersion

Some More Questions From Measures of Dispersion Chapter

Average daily wage of 50 workers of a factory was Rs. 200 with a standard deviation of Rs. 40. Each worker is given a raise of Rs. 20. What is the new average daily wage and standard deviation? Have the wages become more or less uniform?

In the previous question, calculate the relative measures of variation and indicate the value, which in your opinion is more reliable.

If in the previous question, each worker is given a hike of 10% in wages, how are the mean and standard deviation values affected?

The sum of 10 values is 100 and the sum of their squares is 1090. Find the coefficient of variation.

Calculate the mean deviation about mean and standard deviation for the following distribution: Classes Frequencies 20–40 3 40–80 6 80–100 20 100–120 12 120–140 9 50

A measure of dispersion is a good .supplement to the central value in understanding a frequency distribution. Comment

Define dispersion.

How many methods are there to calculate dipersion?

Define range.

Define quartile deviation.

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Calculate the mean deviation about mean and standard deviation for the following distribution:

Classes

Frequencies

20–40

3

40–80

6

80–100

20

100–120

12

120–140

9

50