Question

What is the difference between mean and average?

Answer 1

To solve the question we need to have the clear knowledge of the term mean and average. These are the terms which are used in the same context. Mean is defined as the ratio of the total set of values when the difference between the values are more to the total number of values. Average is defined even in this manner but is valid just for the set of values with small differences.

Complete step-by-step answer:
In this question we are asked to give the difference between the term average and the term mean. Starting with the explanation of AVERAGE:
Average is calculated for the set of the values which has values with less difference in the values. It is defined as the sum of the given numbers divided by the total number of numbers being averaged. In mathematical form it is written as:
Average = $\dfrac{\text{Sum of the given values}}{\text{Total number of values}}$
Let us consider an example to know about the term average:
Let a set of numbers be: $5$, $7$, $12$and $14$.
Total numbers of terms taken in example are $4$.
On applying the formula to find the average we get:
$\Rightarrow \text{Average =}\dfrac{\text{5+7+12+14}}{4}$
$\Rightarrow \text{Average =}\dfrac{38}{4}$
$\Rightarrow \text{Average = 9}.5$

Average is also considered as the Arithmetic Mean.
The next topic for the discussion is Mean.
It is the central point of the set of values. The term "Mean" refers to the addition of the largest and smallest values in the set of numbers and dividing them by two. The formula for the same is:
Mean =$\dfrac{\text{Largest number + Smallest number}}{2}$
On applying the above example of a set of numbers which are $5$, $6$, $9$and $14$ in the above formula for mean, we get:
$\text{Mean}=\dfrac{\text{ Smallest number + Largest number }}{2}$
The smallest and the largest numbers are $5$ and $14$respectively. Putting this in the formula:
$\Rightarrow \text{Mean}=\dfrac{\text{ 5 + 14}}{2}$
Adding the terms in the numerator, we get:
$\Rightarrow \text{Mean}=\dfrac{\text{ 19}}{2}$
$\Rightarrow \text{Mean}=9.5$
Mean refers to the arithmetic mean but it can take other forms too, like harmonic mean, geometric mean etc.

Note: Mean are of basically three types Arithmetic Mean, Geometric Mean and Harmonic Mean. Mean is an important measure because it incorporates the score from every subject in the research study.