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Mean formula
The mean of the data set can be computed by dividing the sum of all the data points by the number of data points. In this article, we learn about the mean formula along with its solved examples for better understanding.
In math, calculating the arithmetic mean is called calculating the arithmetic average. You can determine the sum by adding up all the numbers in a set of data and then dividing it by how many items there are in the set. The arithmetic mean is equal to the middle number for evenly distributed numbers. Depending on how many and in what distribution of data is analyzed, AM can be calculated using various methods.
What is the mean formula?
Using the following formula, you can find the arithmetic mean of a given set of data:
Where,
A- arithmetic mean or average
n- number of items or terms being averaged
x1- value of every single item in the list of numbers being averaged
A= 1/n * x n ∑i=0 xi
Here is a more understandable version of the arithmetic mean formula.
Mean (A) = Sum of all observations (S) / Number of observations (N)
A= S/N
Where,
A- Arithmetic mean or average.
n- number of items or terms being averaged.
S- The sum total of the numbers in the set of interests being averaged.
Solved Examples
Question 1: Find the mean of the following data set.
10, 20, 36, 12, 35, 40, 36, 30, 36, 40
Solution:
Given,
xi = 10, 20, 36, 12, 35, 40, 36, 30, 36, 40
n = 10
Mean = ∑xi/n
= (10 + 20 + 36 + 12 + 35 + 40 + 36 + 30 + 36 + 40)/10
= 295/10
= 29.5
Therefore, the mean of the given data set is 29.5.
Question 2: Find the average of 56, 41, 59, 52, 42 and 44.
Solution: If the given items are very close to each other, a shortcut may be used instead of applying the average formula. Assume that the average is 50, as the terms are around 50 only. Now calculating the difference of all items with 50, you are getting + 6, – 9, +9, + 2, – 8, – 6. Now, if you add these numbers, the result comes out to be – 6. That implies this – 6 will be equally distributed among all the terms and every term will be reduced by – 6/6 = – 1 i.e. average will be reduced by 1. Thus the real average will be 50 – 1 = 49.
