Mean Median Mode Formula

Mean Median Mode Formulas and Solved Examples

The Mean, Median and Mode are basically single value that describes the characteristic of the entire data.

The Mean (Arithmetic mean):

It is found by adding all the numbers in the data set and dividing it by total number of numbers present in data set.
If x1, x2, ….. xn are the values of variable x, then the arithmetic mean usually denoted by $\bar x\,\,{\text{or }}E\left( x \right)$ is given by
$\bar x = \frac{{{x_1} + {x_2} + {x_3} + .... + {x_n}}}{n} = \frac{1}{n}\sum\limits_{i = 1}^n {{x_i}} $
$\sum {x_i}$ represents the sum of all numbers
n represents the number of numbers.
${x_i}$ represent numbers.

The Median:

If the items are arranged in ascending or descending order of magnitude, then the middle value is called Median.
In case of odd number of values
Median = Size of ${\left( {\frac{{n + 1}}{2}} \right)^{{\text{th}}}}$ item.
In case of even number of values
Median = average of $\frac{n}{2}$th and $\frac{{n + 2}}{2}$th item.

The Mode:
The mode is that value in a series of observation which occurs with greatest frequency.

Example:
Find Mean, Median and Mode of data
3, 2, 5, 2, 3, 5, 6, 6, 5, 3, 5, 2, 5.
$Mean = \frac{{{\text{Sum of all numbers}}}}{{{\text{Total numbers}}}} = \frac{{52}}{{13}} = 4$

Median
Arranging in increasing order
2, 2, 2, 3, 3, 3, 5, 5, 5, 5, 5, 6, 6.
So middle term is 5

Mode
Clearly 5 occurs most frequently
So mode = 5.

Practice Question
Find Median of scores 25, 28, 20, 8, 10, 15.
a. 17.5
b. 16.5
c. 20.2
d. 13.5