In order to ascertain whether a distribution is skewed or not the following tests may be applied.

Skewness is present if:

  1. The values of mean, median and mode do not
  2. 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.
  3. The sum of the positive deviations from the median is not equal to the sum of the negative
  4. Quartiles are not equidistant
  5. 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:

  1. The values of mean, median and mode
  2. Data when plotted on a graph give the normal bell-shaped
  3. Sum of the positive deviations from the median is equal to the sum of the negative
  4. Quartiles are equidistant from the
  5. Frequencies are equally distributed at points of equal deviations.