# Help with Sample Skewness

1. Jul 25, 2010

### FrostScYthe

Hi everyone,

I'm using the following formula to calculate skewness

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

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.

2. Jul 28, 2010

### statdad

I believe Excel uses this:

$$\frac n {(n-1)(n-2)} \sum{\left(\frac{x - \bar x}{s}\right)^2}$$

3. Jul 29, 2010

### FrostScYthe

Any particular reason why
excel uses a different formula?

Ted.

4. Jul 29, 2010

### statdad

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.

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