Microsoft Office Tutorials and References
In Depth Information
Deviating from the Middle
The mean of the distribution is 53.669, shown in cell D17. Cells D19 and D20
show the number of values that fall above and below the mean. There are
more values above the mean than below. The distribution, therefore, is
negatively skewed.
The actual skew factor is –0.27323459. The formula in cell D22 is =SKEW
(A1:A1000). The chart makes it easy to see the amount of skew. The plot is
leaning to the right.
Finding out the amount of skew in a distribution can help identify bias in the
data. If, for example, the data is expected to fall into a normal (unskewed)
distribution (such as a random sampling of height for 10-year-old children)
and the data is skewed, then you have to wonder if some bias got into the
data. Perhaps a number of 14-year-old children were measured by mistake
and those heights were mixed in with the data. Of course, being skewed is not
itself an indication of bias. Some distributions are skewed by their very nature.
Here’s how to use the SKEW function to determine the skewness of a
1. Enter a list of numerical values.
2. Position the cursor in the cell where you want the amount of skew to
3. Enter =SKEW( to start the function.
4. Drag the pointer over the list, or enter the address of the range.
5. Enter a ) and press the Enter key.
Another way that a distribution can differ from the normal distribution is
kurtosis. This is a measure of the peakedness or flatness of a distribution
compared with the normal distribution. It is also a measure of the size of the
curves’ tails. You determine kurtosis with the KURT function, which returns
a positive value if the distribution is relatively peaked with small tails
compared with the normal distribution. A negative result means the distribution
is relatively flat with large tails.
Figure 9-11 shows the curves of two distributions. The one on the left has a
negative kurtosis of –0.82096, indicating a somewhat flat distribution. The
distribution on the right is above 1, which means the distribution has a
pronounced peak and relatively shorter tails.
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