Moments

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Distribution Analyses

Moments

The Moments table, as shown in Figure 38.9, includes the following statistics:

N is the number of nonmissing values, n.
Sum Wgts is the sum of weights and is equal to n if no Weight variable is specified.
Mean is the sample mean, ${\overline y}$ .
Sum is the variable sum, ${\sum_{i}^{}{y_{i}}}$ .
Std Dev is the standard deviation, s.
Variance is the variance, s².
Skewness is the sample skewness, g₁.
Kurtosis is the sample kurtosis, g₂.
USS is the uncorrected sum of squares, ${\sum_{i}^{}{y_{i}^2}}$ .
CSS is the sum of squares corrected for the mean, ${\sum_{i}^{}{( y_{i}-{\overline y})^2}}$ .
CV is the percent coefficient of variation, $100 s/{\overline y}$ .
Std Mean is the standard error of the mean, ${s/\sqrt{n}}$ . The value is set to missing if vardef ${\ne}$ DF.

dist09.gif (10798 bytes)

Figure 38.9: Moments and Quantiles Tables

For weighted analyses, the Weighted Moments table includes the following statistics:

N is the number of nonmissing values, n.
Sum Wgts is the sum of weights, ${\sum_{i}^{}{w_{i}}}$ .
Mean is the weighted sample mean, ${{\overline y_{w}}}$ .
Sum is the weighted variable sum, ${\sum_{i}^{}{w_{i} y_{i}}}$ .
Std Dev is the weighted standard deviation, s_w.
Variance is the weighted variance, s²_w.
Skewness is the weighted sample skewness, g_w1.
Kurtosis is the weighted sample kurtosis, g_w2.
USS is the uncorrected weighted sum of squares, ${\sum_{i}^{}{w_{i} y_{i}^2}}$ .
CSS is the weighted sum of squares corrected for the mean, $\sum_{i}^{}{w_{i} ( y_{i}-{\overline y_{w}})^2}.$
CV is the percent coefficient of variation, $100 s_{w}/{\overline y_{w}}$ .
Std Mean is the standard error of the weighted mean, ${ s_{w}/\sum_{i}^{}{w_{i}}}$ .
The value is set to missing if vardef ${\ne}$ DF.

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