Measuring Statistical Variation
- From: "Leonard M. Wapner" <lwapner@xxxxxxxxxxxxxx>
- Date: Sat, 29 Sep 2007 19:17:57 -0700
We're given a sample of single variable numerical data that is bimodal.
The values range from 0 to 10 but they are clustered around 2 and 9. So,
the sample data might look something like -
{0, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 5, 7, 8, 8, 9, 9, 9, 9, 9,
9, 9, 9, 9, 9, 10}.
The standard deviation (and variance) for this sample would be relatively
large, compared to a normally distributed sample having the same range and
mean. This is as it should be; the data is, in a sense, spread out when
compared to normally distributed data.
But in another sense, there is less variation due to the clumpiness of the
data. It is tightly packed together in two clumps with little spread
beyond the modes. Standard deviation and variance fail to detect this.
Is there a statistic which measures, or reflects the clumpiness?
Thanks -
Len
.
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