# Skewness

A normal distribution is a bell-shaped distribution of data where the mean, median and mode all coincide. A frequency curve showing a normal distribution would look like this:

Image

In a normal distribution, approximately 68% of the values lie within one standard deviation of the mean and approximately 95% of the data lies within two standard deviations of the mean.

If there are extreme values towards the positive end of a distribution, the distribution is said to be positively skewed. In a positively skewed distribution, the mean is greater than the mode. For example:

Image

A negatively skewed distribution, on the other hand, has a mean which is less than the mode because of the presence of extreme values at the negative end of the distribution.

There are a number of ways of measuring skewness:

 Pearson’s coefficient of skewness = mean – mode = 3(mean – median) Standard deviation Standard deviation

 Quartile measure of skewness = Q3 – 2Q2 + Q1 Q3 – Q1

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