In order to ascertain whether a distribution is skewed or not the following tests may be applied.
Skewness is present if:
- The values of mean, median and mode do not
- When the data are plotted on a graph they do not give the normal bell- shaped form i.e. when cut along a vertical line through the centre the two halves are not equal.
- The sum of the positive deviations from the median is not equal to the sum of the negative
- Quartiles are not equidistant
- Frequencies are not equally distributed at points of equal deviation
On the contrary, when skewness is absent, i.e. in case of a symmetrical distribution, the following conditions are satisfied:
- The values of mean, median and mode
- Data when plotted on a graph give the normal bell-shaped
- Sum of the positive deviations from the median is equal to the sum of the negative
- Quartiles are equidistant from the
- Frequencies are equally distributed at points of equal deviations.