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 x_{1}, x_{2}, ….. x_{n} 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