# Measures of Central Tendency

Here we will study different **Measures of Central Tendency**. The Measure of central tendency or averages is also known as Measures of locations. It is a single value which represents the whole set of data. Since it represents entire data so its value lies somewhere in between the two extreme values of the data. In other words, the tendency of data to cluster around a figure which is in the central location is known as the central tendency.

## Types of Average

Averages are broadly classified into two main categories

**1. Mathematical Average**

**2. Positional Average**

There are some other averages also, termed as **Miscellaneous Average**.

## Requisites of a Good Average

The following are the requisites of a good average:

1. It should be simple to calculate and easy to understand.

2. It should be based on all values.

3. It should not be affected by extreme values.

4. It should not be affected by sampling fluctuation.

5. It should be strictly defined by an algebraic formula so that different persons obtain the same value for a given set of data.

6. It should have sampling stability.

## Rules of using ∑:

If c be a constant, then

\[\sum\limits_{i=1}^{n}{c=nc}\]

\[\sum\limits_{i=1}^{n}{c{{x}_{i}}=c\sum\limits_{i=1}^{n}{{{x}_{i}}}}\]

\[\sum\limits_{i=1}^{n}{({{x}_{i}}\pm {{y}_{i}})=\sum\limits_{i=1}^{n}{{{x}_{i}}}}\pm \sum\limits_{i=1}^{n}{{{y}_{i}}}\]