Skewness is a measure of symmetry of a frequency distribution. Symmetrical distributions have a "hump" in the middle of the distribution and a "tail" on either side of the hump. These have a skewness of zero. Distributions with a large number of frequency scores clustered at the lower end of the distribution have a "tail" pointing toward higher values and a "hump" over the smaller values. This is said to be positively skewed. When the frequency scores are clustered at the higher end of the distribution, the "tail" points toward the lower values and the "hump" is centred over the larger values. This is said to be negatively skewed. Skewness can be calculated from computer programs or by hand.
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Things you need
Calculate the mean and standard deviation from the raw scores, or numbers, in a given set of data.
List the raw scores in a column.
Subtract the mean from each raw score and list these numbers in a separate column. These numbers are called deviations from the mean.
Raise each deviation to the third power and list these numbers in a third column.
Add the cubed deviations in the third column together. This is called the sum of the third moment deviations.
Count the number of scores in the dataset and subtract one from this number.
Raise the standard deviation to the third power.
Multiply the number of scores minus one by the cubed standard deviation.
Divide the sum of the third moment deviations by the number of scores minus one times the cubed standard deviation.
Tips and warnings
- A positive value of skewness comes from a large number of values above the mean, which leads to a "tail" pointing toward the smaller numbers and indicates a negatively skewed distribution.
- A negative value of skewness comes from a large number of values below the mean, which leads to a "tail" pointing toward the larger numbers, and indicates a positively skewed distribution.
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