# Mean

## Overview

When there is many elements in a dataset, it would be useful to have a measure that best represents the dataset. Such a measure would be the central element in within the data data-set. When the data has a normal distribution this central tendency could be best described by the average. In statistics the more formal term for average is mean ($\bar{x}$$\bar{x}$).

The mean is the sum of all the data elements (x1…xn) divided by the count (n). This can be mathematically represented as follows:

$\bar{x}=\frac{1}{n}\sum_{i=0}^{n}{x}_{i}=\frac{1}{n}\left({x}_{1}+{x}_{2}+{x}_{3}\cdots +{x}_{n} \right)$$\bar{x}=\frac{1}{n}\sum_{i=0}^{n}{x}_{i}=\frac{1}{n}\left({x}_{1}+{x}_{2}+{x}_{3}\cdots +{x}_{n} \right)$

Where,
${x}_{1}=$${x}_{1}=$ first element

${x}_{n}=$ last element

${n}=$ count

Example 1.
The weight (kg) of children in a small class is as follows: 17.1, 15.4, 13.5, 18.7,19.4. What is the average weight of the children in the class?

Answer.

The cunt (n)

${n}=5$${n}=5$

The sum of the weights:

$\sum_{i=1}^{5}=17.1 + 15.4 + 13.5 + 18.7 + 19.4=84.1$$\sum_{i=1}^{5}=17.1 + 15.4 + 13.5 + 18.7 + 19.4=84.1$

The mean:

$\bar{x}=\frac{84.1}{5}=16.82$$\bar{x}=\frac{84.1}{5}=16.82$

Last updated byGanealingam Narenthiran on March 23, 2020

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