What is Mean in Statistics (Formula, Calculation, Examples & Properties)

What is a Mean?

Mean is the average of the given numbers which is calculated by dividing the sum of given numbers by the total count of numbers. 

Example: 

Find the mean of the given numbers 2, 4, 4, 4, 5, 5, 7, and 9?

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Solution:

• Step1: Take sum of all numbers, 2 + 4 + 4 + 4 + 5 + 5 + 7 + 9 = 40
• Step2: Divided sum by the total count of numbers, 40/ 8 = 5

 Properties of Mean: 

1. The mean (or average) is the most popular and well-known measure of central tendency.
2. It can be used with both discrete and continuous data, although its use is most often with continuous data.
3. There are other types of means. Geometric mean, Harmonic mean, and Arithmetic mean.
4. Mean is the only measure of central tendency where the sum of the deviations of each value from the mean is always zero.

How to find Mean of ungrouped data:

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How to find Mean of grouped data:

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How to find Mean in an array?

Given the n size array, find its mean.
Examples:

Input  : {1, 3, 4, 2, 6, 5, 8, 7}
Output : Mean = 4.5
Explanation: Sum of the elements is 1 + 3 + 4 + 2 + 6 + 5 + 8 + 7 = 36, Mean = 36/8 = 4.5

Input  : {4, 4, 4, 4, 4}
Output : Mean = 4

Approach:

Formula used:

Mean of an array = (sum of all elements) / (number of elements)

Follow the steps below for implementation:

• Iterate over the array and keep adding elements to a variable sum
• Divide the sum by the size of given array.

Below is the implementation of the above approach

Mean = 4.5

Time Complexity: O(n), Where n is the size of the given array.
Auxiliary Space: O(1), As no extra space is used.

Basic Program related to Mean 

• Find mean of subarray means in a given array
• Mean of array using recursion
• Find the mean vector of a Matrix
• Mean of range in array
• Mean and Median of a matrix

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