Question

For a frequency distribution mean is
120 mode is 90 and Pearson's
coefficient of skewness is 0.5 then
the standard deviation is​

Answer 1

Explanation:

6uuMean - mode = 3 (mean - median)

100−mode=3(100−98.5)

Mode =100−4.5

=95.5

Sk

p

=

S.D.

Mean−Mode

=

9

100−95.5

=

9

4.5

=0.5

Sk

p

>0, the distribution is positively skewed.

Answer 2

Given: Frequency distribution mean, M = 120

           Frequency distribution mode, m  = 90

           Cofficient of skewness, Sk  = 0.5

To Find: Standard deviation, S.D.

Solution:

To calculate S.D., the formula used:

• In statistics, Standard deviation is the measure of the dispersion of a dataset in relation to the mean of that dataset.
• It shows, how a particular data is scattered or varies from its value.

• Coefficient of skewness, Sk = (Mean - Mode) / standard deviation
• Sk = (M-m) / S.D.

Applying the above formula:

0.5 = ( 120 - 90) / S.D.

0.5 = 30 / S.D.

S.D. x 0.5 = 30

S.D. = 30/ 0.5

       = 30x10/ 5

       = 300/ 5

       = 60

S.D. = 60

Hence, standard deviation is 60.