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Measures Of Dispersion

Question
CBSEENST11024839
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The Standard Deviation of height measured in inches will be larger than the Standard Deviation of the height measured in ft. for the same group of individuals. Comment on the validity or otherwise of the statement with appropriate illustration.

Solution

The statement is totally valid. The least is that Standard Deviation is an absolute measure. When the units of measurement are different the less the measurement will, the more will the Standard Deviation. With the increase in the measurement unit, the Standard Deviation will decrease. It is clear from the following illustrations.

Suppose we are given the heights of 5 persons in feet. such as 2, 4, 6, 8, 10. With the help of the data we will calculate the S.D.

Height in feet

D

D2

(X)

 

2

–4

16

4

–2

4

6

0

0

8

2

4

10

4

16

ΣX = 30

  

ΣD2 = 40

Now we calculate S.D. taking the heights of 5 same persons in inches.

Height in inches

D

D2

(X)

 

24

–48

2304

48

–24

576

72

0

0

96

+24

576

120

+48

  

ΣX = 360

  

ΣD2 = 5760

Thus, we see that S.D. has increased 12 times.

Some More Questions From Measures of Dispersion Chapter

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.

How is coefficient of quartile deviation calculated?

Define mean deviation.

 

Define standard deviation.

Give formula to calculate standard deviation of a frequency destribution series by direct method.

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