Measures of Central Tendency

A measure of central tendency is a typical value that represents the entire mass of unwieldy data and is also known as averages. As average is a single value representing a group of values & tends to lie within the mass of data arranged in order of magnitudes.

The objectives of studying the measures of central tendency are:

• to locate the distribution
• to represent the mass of data by a single typical value
• to measure the central value around which the data tend to cluster and
• to compare distributions of the same type

Properties of Good Measures of Central Tendency

To get an ideal measure of central tendency, it must satisfy following properties as far as possible.

1. It should be easy to understand.
2. It should be simple to compute.
3. It should be rigidly defined. The average computed for a given data should for a different people be the same definite value.
4. It should be unaffected by extreme items (i.e. largest or smallest value).
5. It should be based on all observations. For an average to calculate, it should be computed by including all the items as far as possible.
6. It should have sampling stability.
7. It should be capable of further algebric treatment.

TYPES OF MEASURES OF CENTRAL TENDENCY

The types of measures of central tendency are:

1. Arithmetic Mean (A.M.)
2. Median (M_d)
3. Mode (M_o)
4. Geometric Mean (G.M.)
5. Harmonic Mean (H.M.)

THe first three are the most common measures of central tendency.

Arithmetic Mean

It is the most popular and commonly used statistical average. It is defined as the ratio of the total values to the number of values i.e.

$$ Arithmetic Mean = \frac {Sum of Values}{Number of Values}$$