**Definition:**

A

*measure of central tendency*is a typical value around which other figures congregate that attempts to describe a set of data by identifying the central position within that set of data.

As such, measures of central tendency are sometimes called measures of central location.

**Types of measures of central tendency:**

The most commonly used measure of central tendency are

1. Mean

2. Median

3. Mode

1.

**Mean:**Mean is the most common measure of central tendency. It is simply the sum of the numbers divided by the number of numbers in a set of data. This is also known as average.

If we have n values in a data set and they have values x1, x2, ..., xn, then the sample mean, usually denoted by (pronounced x bar), is:

2.

**Median:**Median is the number present in the middle when the numbers in a set of data are arranged in ascending or descending order. If the number of numbers in a data set is even, then the median is the mean of the two middle numbers.

3.

**Mode:**Mode is the value that occurs most frequently in a set of data.

Examples of Measures of Central Tendency

For the data 1, 2, 3, 4, 5, 5, 6, 7, 8 the measures of central tendency are

Mean = (1+2+3+4+5+6+7+8)/8=4.56

Median = 5

Mode = 5

The mean can again be of three types

1. Arithmetic mean

2. Geometric mean

3. Harmonic mean

1. Arithmetic mean:

A mathematical representation of the typical value of a series of numbers, computed as the sum of all the numbers in the series divided by the count of all numbers in the series.

Arithmetic mean is commonly referred to as "average" or simply as "mean".

A Measures of Central Tendency is a single value which is used to define the set of data by knowing the central position within the set of given data. It is also known as measure of central location. Mean, mode and median are all the Measures of Central Tendency but in some of the conditions some of the Measures of Central Tendency are difficult to use with compare to other.

ReplyDeleteA measure of central tendency is any of a number of ways of specifying this "central value". It is an important term used in Statistics.

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