Understanding Skewness in Excel

[FrostScYthe]

Hi everyone,

I'm using the following formula to calculate skewness

g_1 = \frac{m_3}{m_2^{3/2}} <br /> = \frac{\tfrac{1}{n} \sum_{i=1}^n (x_i-\overline{x})^3}{\left(\tfrac{1}{n} \sum_{i=1}^n (x_i-\overline{x})^2\right)^{3/2}}\ ,

However, when I try excel on to calculate skewness I get a different results. For example this set:

1
1
1
1
1
1
1
9
9

I get: 1.33630621
Excel gets: 1.619847741

Is excel using a different formula, or am I doing something wrong?

Ted.

 

[statdad]

I believe Excel uses this:

<br /> \frac n {(n-1)(n-2)} \sum{\left(\frac{x - \bar x}{s}\right)^2}<br />

 

[FrostScYthe]

Any particular reason why
excel uses a different formula?


Ted.

 

[statdad]

Any particular reason why
excel uses a different formula?


Ted.

I can't really answer why their choice was made. Note that unlike the mean (for example) there are several quantities proposed to estimate skewness, and none is really preferred as "the correct way" to do it.