# Measures of Central tendency

Measures of Central tendency

They are also known as statistical average. They are statistical values which tend to occur at the centre of any well-ordered data. However, whenever they occur they do not indicate the centre of that data. They tell us the point about which items have a tendency to cluster. Such measures are considered as the most representative figure for the entire mass of the data.

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Measures of central tendency include:

Mean

Mode

median

Mean

Mean is also known as arithmetic average. It may be defined as the value which we get by dividing the total values of the given observations in a series by the total number of the observations.

Arithmetic mean = (?x)/n ; where x is the number of values and n is the number of observations.

Arithmetic mean represents the values of the most observations in a given population.

In grouped data, arithmetic mean is calculated as:

Arithmetic mean = Assumed mean + (?fd)/(?f)

The Mode

This is the value within a frequency distribution which has the highest frequency. On a histogram, it represents the highest bar in a bar chart. It is the most commonly or frequently occurring value in a series. The mode in a distribution is that item around which there is maximum concentration hence it is the size of the item which has the maximum frequency.

In data where no single value happens to be the mode, the class with the highest frequency is treated as such – referred to as the modal class.

The Median

Median is a statistical value which is normally located at the centre of a given set of data which has been organized in ascending or descending order of magnitude or size. It divides the series into two halves.

Suppose we are asked to calculate the median in the data below:

65 55 89 92 56 35 14 56 55 87 45 92

We first need to rearrange the data in order of magnitude (smallest first)

14 35 55 55 56 56 65 87 89 92 92

Our median mark is the middle mark in this case 56