Unimodal Distribution – Locations of the Mean, Mode and the Median

A unimodal distribution is a distribution that has one clear peak. The values increase first, rising to a single highest point where they then start to decrease. A unimodal distribution can either be symmetrical or nonsymmetrical.

A symmetrical distribution is one where the mean, mode, and median are all equal. In such a distribution, the intervals of gains or losses exhibit the same frequency. For instance, if we have a symmetrical distribution with a mean return of zero, then the frequency of losses between -2% and -1% will be equal to the frequency of gains between 1% and 2%.

A distribution that deviates from the symmetrical distribution is said to be nonsymmetrical, and that’s how we end up having positive skewness and negative skewness.

Unimodal Distribution – Positively Skewed

This is the tendency of a given frequency curve leaning towards the left. Conversely, the ‘tail’ extends to the right. In this distribution, candidates should note the following:

1. The mean is bigger than both the median and the mean.
2. The median always occurs between the mode and the mean.
3. The observations below the mean are more than those above it.

A good example of a positively skewed distribution would be the age distribution in a developing country.

Unimodal Distribution – Negatively Skewed

This is a frequency curve where the long tail extends to the left. It has the following characteristics:

1. The mode is usually bigger than both the median and the mean.
2. The median is found between the mean and the mode.
3. The observations above the mean are usually more than those below it.

A good example of a negatively skewed distribution would be the age distribution in a developed country.