∑

x-O1

n

Population

VARIANCE

Kth MomentaboutT =

1st MomentaboutO =

Mean

2nd Momentaboutmean =

∑

x-x

2

n

∑

x-T

k

n

The third momentabout the meanis relatedto the asymmetryor skewnessof a

distribution:

Aunimodal(i.e. a singlepeaked)distributionwith µ3< 0 is said to be skewed to

the left — that is, it has a left "tail".If µ3> 0, the distributionis skewed to the

right.

For symmetricdistributionµ3= 0

Skewness=β=μ3
1s

The quantity measuresthe skewnessof the distributionrelativeto its degreeof

spread.This standardizationallows us to comparethe symmetryof two

distributionswhosescalesof measurementdiffer.

3

μ
3=(x-x
∑)3
n