162 Fundamentals of Statistics
Measures of Shape: Skewness and Kurtosis
You’ve seen that different distributions can be characterized by their shape.
For example, a distribution may be skewed positively or negatively or may
be symmetric about its midpoint. These visual judgments we make of a dis-
tribution’s shape also can be quantifi ed with a statistic. One of these is the
skewness statistic. Skewness is a measure of the lack of symmetry in the
distribution of the data values.
A positive skewness value indicates a distribution with values clustered
toward the lower range of values with a long tail extending toward the up-
per values’ range. A negative skewness indicates just the opposite, with the
long tail extending toward the values lower in the data range. A skewness of
zero indicates a symmetric distribution.
Another statistic, kurtosis, measures the heaviness of the tails in the dis-
tribution. A positive kurtosis indicates more extreme values than expected
in the distribution. A negative kurtosis indicates fewer extreme values than
expected. Table 4-7 shows the Excel functions used to calculate skewness
and kurtosis.Table 4-7 Excel functions to calculate skewness and kurtosis
Function Description
KURT(array) Returns the kurtosis of the values in an array
or data range.
SKEW(array) Returns the skewness of the values in an array
or data range.Use the Univariate Statistics command from the StatPlus menu to
calculate the variability and shape statistics for the prices of homes in the
Albuquerque sample.To create a table of variability and shape statistics:1 Click Descriptive Statistics from the StatPlus menu and then click
Univariate Statistics.
2 Click the Input button and select Price from the list of range names.
3 Click the Output button, click the New Worksheet option button,
and type Price Variances in the New Worksheet box. Click the OK
button.
4 Click the By button and select NE_Sector from the list of range names.
5 Click the Variability dialog tab.
6 Click the Show all variability statistics checkbox. See Figure 4-22.