7- Distributions
Symmetrical Distribution: When a distribution is symmetrical, the mode, median and mean are all in the middle of the distribution. The following graph shows a larger retirement age data-set with a distribution which is symmetrical. The mode, median and mean all equal 58 years.
Skewed Distribution: When a distribution is skewed the mode remains the most commonly occurring value, the median remains the middle value in the distribution, but the mean is generally ‘pulled’ in the direction of the tails. In a skewed distribution, the median is often a preferred measure of central tendency, as the mean is not usually in the middle of the distribution.
A distribution is said to be positively or right skewed when the tail on the right side of the distribution is longer than the left side. In a positively skewed distribution it is common for the mean to be ‘pulled’ toward the right tail of the distribution. Although there are exceptions to this rule, generally, most of the values, including the median value, tend to be less than the mean value.
Kurtosis Distribution: It is a measure of the “tailedness” of the probability distribution of a real-valued random variable.
