Raw Moments

The nth raw moment about zero is the expected value of Xⁿ.

1^st raw moment:

2^nd raw moment = mean

3^rd raw moment:

4^th raw moment:

For the data (1, 2, 2, 4, 6), the raw moments can be found as follows:

Central Moments

Central moments are moments about the mean.

1^st central moment (m₁)

2^nd central moment (m₂) = variance

3^rd central moment (m₃)

4^th central moment (m₄)

For the data (1, 2, 2, 4, 6), the mean is 3. Therefore,

Standardized Moments

The standardized moment is a moment that has normalized.

1^st standardized moment (a₁)

2^nd standardized moment (a₂)

3^rd standardized moment (a₃)

4^th standardized moment (a₄)

For the data (1, 2, 2, 4, 6), the mean is 3 and the standard deviation is 1.79. Therefore,