## MEASURES OF CENTRAL TENDENCY IN STATISTICS

Measures of Central Tendency are the expected values of the variable or is a value in a data around which the items of the data congregate. It represents the whole set of data. The Measures of Central Tendency is also known as an ‘Average’ or ‘Measures of Location.’

**ACCORDING TO SIMPSON AND KAFKA**

“A measure of central tendency is a typical value around which other figures congregate.”

Thus, Measures of Central Tendency are the values which lie between the two extreme observations i.e. largest and smallest observations of the distribution.

## VARIOUS MEASURES OF CENTRAL TENDENCY

The various measures of central tendency are as follows:

## MATHEMATICAL AVERAGES

#### ARITHMETIC MEAN

Arithmetic Mean is the number which is obtained by adding the values of all the items of a series and dividing the total by number of items. It is also called ‘Common Average.’ It is of two types:

- Simple Arithmetic Mean
- Weighted Arithmetic Mean

#### GEOMETRIC MEAN

Geometric Mean is the *n*th root of the product of *n*
items in a given series. The geometric mean is obtained by multiplying the
values of the items together and then taking it to its root corresponding to
the number of items.

#### HARMONIC MEAN

Harmonic mean of a given series is the reciprocal of the arithmetic average of the values of its various items.

**ACCORDING TO W I GREENWALD**

“The harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocal of the series.”

## POSITIONAL AVERAGES

#### MEDIAN

Median is the middle value of a distribution when the series is arranged in ascending or descending order. It is the value which divides the whole series into two equal parts. Thus, in case of median, the number of items less than median and the number of items more than median will be equal.

#### MODE

Mode is the value which occurs most frequently in a statistical distribution. The word ‘Mode’ is derived from the French word ‘la made’ which means ‘Fashion’ or the most popular phenomenon. So mode can be known from a value which occurs frequently.

Also Study: | Also Study: | Also Study: | Also Study: | Also Study: |

Measures of central tendency | Arithmetic Mean | Median | Mode | Statistics |

Functions of statistics | Scope of statistics | Limitations of Statistics | Distrust of statistics |

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