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

Step-by-step explanation:

mean=120

Skp=0.5

mode=90

S.D=120-90/0.5

=60

Answer 2

The standard deviation of the distribution is 60.

For a frequency distribution mean is 120, mode is 90 and Pearson's coefficient of skewness is 0.5.

We have to find the standard deviation.

Karl Pearson's Coefficient of Skewness is used to measure asymmetry in the distribution.

• When skewness is positive, longer tail will appear to the right.
• When skewness is negative, longer tail will appear to the left.
• And when skewness is zero, it will show a perfectly symmetry distribution. (see graph mentioned in answer to understand better).

According to Karl Pearson,

coefficient of skewness = (mean - mode)/standard deviation

here, mean = 120, mode = 90 and coefficient of skewness = 0.5

∴ standard deviation = (120 - 90)/0.5

= 30/0.5 = 60

Therefore the standard deviation of the distribution is 60.