A measure of central tendency (measure of center or central location) is a summary measure that attempts to describe a whole set of data with a single value that represents the middle /centre distribution.

The main measures of central tendency are: The mode, the median, and the mean.

**i. The mode:** This refers to the commonly occurring value in a distribution. For example, the mode in the following distribution (54,54,55,56,57,57,57,57,60,60) is 57, which occurs 4 times. The main advantage of mode over the median and the mean is that it can be found for both numerical and categorical (non-numerical) data.

Limitation of mode

â€¢ In some distributions, the mode may not reflect the centre of the distribution very well -as the mode may be higher or lower than the centre of the distribution when the data is ordered from lowest to the highest.

â€¢ There can be more than one mode for the same distribution data (bi-modial or multi-modia), thereby limiting the ability of the mode in describing the centre of the distribution as the centre cannot be identified.

â€¢ In some cases, particularly where the data are continuous, the distribution may have no mode at all (i.e. if all values are different).

**ii. The median:** The median refers to the middle value in distribution when the values are arranged in ascending or descending order. The median divides the distribution in half. For example, the median in this distribution date (54,54,55,56,57,57,57,57,60,60) is 57. The main advantage of the median is that it is less affected by outliers and skewed data than the mean and is therefore the preferred measure of central tendency when the distribution is asymmetrical.

Limitation of median

â€¢ The median cannot be identifying for categorical nominal data as it cannot be logically ordered.

**iii. The mean:** The mean (arithmetic mean) refers to the sum of the value of each observation in a dataset divided by the number of observations. For example, the mean of the following distribution date (54,54,55,56,57,57,57,57,60,60) =567/10 =56.7.

The main advantage of mean is that it can be used for both continuous and discrete numeric data.

Limitations of mean

â€¢ The mean cannot be calculated for categorical data, as the values can be summed

â€¢ The mean is influenced by outliers and skewed distributions as it includes every value in the distribution.