# Mean in Statistics

In Statistics, a mean also known as, average, is a measure of the central tendency of a given set of values. In other words, the mean is the average of a given data set.

## Types of Mean

There are three different types of mean namely:

1. Arithmetic Mean
2. Geometric Mean
3. Harmonic Mean

1. Arithmetic Mean

If we add up all the values and divide by the number of values, then it is termed the arithmetic mean. To calculate the arithmetic mean, add all the numbers and divide by how many numbers are given in a set.

Example: What is the mean of 2, 5, 7, 5, 9, 3?
Solution:
Now add up all the given numbers:
2 + 5 + 7 + 9 + 3 + 5= 30

Now divide by how many numbers are provided in the sequence:

30/ 6 = 3

2. Geometric Mean

The geometric mean of two numbers p and q is pq. The geometric mean of three numbers p,q, and r is 3pqr.
Geometric Mean = nx₁x₂x₃…. xn

Example: Find the geometric mean of 9 and 3.

Solution:
Geometric Mean: 9 × 3 = 33 = 3 1.732 = 5.196

3. Harmonic Mean:

The harmonic mean of two numbers p and q is 2pq( p + q). The geometric mean of three numbers p,q, and r is 3pqr (pq + qr+ rq).

Harmonic Mean: n1x1 + 1×2 + 1×3 + …..1xn

## How s Mean Calculated?

Mean is defined as the sum of all observations divided by the number of observations.

The formula to find “Mean” is given as:

Mean Formula: Sum of All ObservationsNumber of Observation

## How is Mean Represented?

If we are finding the mean for a data represented by the measurements k₁, k₂,k₃, the mean is written as x and pronounced as x – bar. Therefore, for the given data k₁, k₂,k₃, the mean is calculated as:

x = k₁+  k₂ + k₃ +……+knn

## Example

Example 1: What is the mean of values ( 3, 4, 5, 2, 1)?

Solution:

There are total of 5 values.

Therefore, the mean is 3 + 4 + 5 + 2 + 15

= 155

= 3

## Formula to Calculate Mode

The different mode formulas in individual, continuous, and discrete series are:

• Individual Series: In this series, observe the maximum number of times an individual observation occurs.
• Discrete Series: In this series, observe the highest frequency of the observations.
• Continuous Series: The formula to calculate mode in continuous series:

l + fi = f02f1 – f2- f0h

•       l = It indicates the lower limit of the modal class.
• f1 = It indicates the frequency of the modal class.
• f2 = It indicates the frequency of the class interval succeeding the modal class;
• f0=  It indicates the frequency of the class interval preceding the modal class
• h = It is the width of the class interval.

## Mode Example

### Practical Example: What is the mode of the following distribution:

1,2,3,5,5,5,7,8,2,9,5,3,4,9,1

As we know, mode is the observation that occurs most frequently in a frequency distribution. As we can see, in the given frequency distribution 5 occurs the maximum number of times. Hence, the mode of given frequency distribution is 7. This is a very useful topic, and you can learn it easily at Cuemath.