## Introduction

To understand the difference between mean and average, we must understand what both of them are. A lot of time, the Mean and Average are used interchangeably. Average is usually used in general day-to-day conversations, while the mean is used in statistical and technical terms.

Comprehending the difference between Mean and Average is crucial since sometimes it may improve our understanding.

## What is Mean?

Mean is an essential concept in Statistics and Mathematics. Mean is used in the measurement of central tendency. In terms of statistics, the mean for a given set is equal to the sum of all the values in the set divided by the total number of values in that particular set.

There are three most used ways to calculate the mean of the dataset. For simplification, let us consider a set of 'n' elements with values 2, 7, 9, 10, and 15. We will use the same example for our calculations below.

### Arithmetic Mean

It is the simplest of all three and is just the sum of all values in a set divided by the total number of values.

Now, letâ€™s find out the arithmetic mean for our dummy example.

Sum = (x1 + x2 + x3 + x4 + x5) = (2 + 7 + 9 + 10 + 15) = 43 and n = 5

Arithmetic mean = 43 / 5 = 8.6

The arithmetic mean is useful when the data is evenly distributed, as it can be easily distorted if the set contains some outliers.

### Geometric Mean

The geometric mean is the nth root of the product of all n values, where n is the number of values in the set.

Let's calculate the Geometric mean for the above example:

Geometric mean = (2 * 7 * 9 * 10 * 15) ^ (1 / 5)

= (18900) ^ (1 / 5)

= 7.16625

The geometric mean does not allow negative values to avoid complications of imaginary roots. It only contains positive values into consideration for calculation. The geometric mean is usually used in growth rates, like population growth, interest rates, and stock prices.

### Harmonic Mean

Harmonic Mean is the reciprocal of the average of reciprocals of all the numbers in the set. Like the geometric mean, the harmonic mean does not consider negative or zero values for calculation. The harmonic mean is used in situations rate of change or average rate and ratios need to be calculated.

Now, let's calculate the harmonic mean of the same example.

Denominator = ((1 / 2) + (1 / 7) + (1 / 9) + (1 / 10) + (1 / 15))

= 0.5 + 0.142 + 0.111 + 0.1 + 0.066

= 0.919

Harmonic mean = 5 / 0.919 = 5.44