## How to find Mean?

Mean means the even distribution of values for a given data set.

It is nothing but the average of the given set of values.

In statistics, the mean is one of the measures of central tendency, apart from the mode and median.

## Definition of Mean

Mean is the average of the numbers that are given.

It is calculated by dividing the total of the numbers that are given by the total number of numbers

## Example

Q. What is the mean of 2, 4, 6, 8 and 10?

A. The 1^{st} step is to add all the numbers.

2 + 4 + 6 + 8 + 10 = 30

Now divide the total i.e. 30 by five (total number of observations).

Mean = 30/5 = 6

## Symbol

The mean symbol is typically denoted by the symbol ‘x̄’.

The bar or the viniculum over the letter x, represents the mean of x no of values.

X̄ = (Sum of the given values ÷ Number of the given values)

X̄ = (x1 + x2 + x3 +….+xn) / n

## Formula

The basic formula to calculate mean is calculated based on the given nos or the given data set.

Each term in the data set is considered when one is trying to evaluate the mean.

The general formula for calculating the mean is given by the ratio of the total of all the nos and the total no of terms.

Hence, we can say;

Mean = Total of the Given Numbers/ Total number of Data

To calculate the mean of a set of nos, we must 1^{st} add up (sum) all of the data values (x) and then divide the total by the no of values (n).

Since ∑ is the symbol used to denote the values (that are supposed to be summed (see Sigma Notation), you obtain the following formula for the mean (x̄):

x̄=∑ x/n

## How To Find Mean?

As we know, data can be either in grouped form or ungrouped form.

So, to find the mean of given numbers, you are required to check whether the given data is ungrouped or grouped.

The formulas for finding the mean for grouped data and ungrouped data are different.

In the slides that follow, you will learn the method to find the mean for both of these.

## Mean For Ungrouped Data

The example given below will help you in understanding how to find the mean of ungrouped data.

Q. In a class there are 20 students and they have secured a percentage of 88, 82, 88, 85, 84, 80, 81, 82, 83, 85, 84, 74, 75, 76, 89, 90, 89, 80, 82, and 83.

Find the mean percentage obtained by the class.

Mean = Total of percentage obtained by 20 students in class/Total number of students

= [88 + 82 + 88 + 85 + 84 + 80 + 81 + 82 + 83 + 85 + 84 + 74 + 75 + 76 + 89 + 90 + 89 + 80 + 82 + 83]/20

= 1660/20

= 83

Hence, the mean percentage of each student in the class is 83%.

## How to find Mean For Grouped Data

**Q. **Find the mean of the given data –

x_{i} | 11 | 14 | 17 | 20 |

f_{i} | 3 | 6 | 8 | 7 |

x_{i} | f_{i} | f_{i}x_{i} |

11 | 3 | 33 |

14 | 6 | 84 |

17 | 8 | 136 |

20 | 7 | 140 |

∑f_{i} = 24 | ∑f_{i} x_{i }= 393 |

Mean = ∑fixi/∑fi = 393/24 = 16.4

## How to find Mean For Negative Numbers

We have observed numerous examples of finding the mean of positive nos till now.

But what if the nos in the observation list include negative nos?

Let us understand with an example:

Find the mean of 9, 6, -3, 2, -7, 1.

Add all the given nos 1^{st}:

Sum: 9+6+(-3)+2+(-7)+1 = 9+6-3+2-7+1 = 8

Now you should divide the total from six, to obtain the mean.

Mean = 8/6 = 1.33

## Real – Life Applications Of Mean

In this real world, where there is huge amount of data available, we use statistics to deal with it.

Suppose, in a data table, the price values of ten clothing materials are mentioned.

If we have to find the mean of the prices, then add the prices of each clothing material and divide the total by ten. It will result in a mean value or an average value.