 # Mean , Median ,Mode and Range Calculator

Note
• Enter the values of the numbers seperated by commas whose average need to be found Example 2,3,4
• Click on the calculate button.

Formula And concept used
Mean is the sum of all the values divided by the number of values $Mean = \frac {x_1 + x_2 + x_3 +..+x_n}{n}$

Median is the middle-value in the list of numbers which is derived by sorting the list by ascending order and then select the middle one.

Mode is the value which is repeated maximum times.

Range is the difference of maximum and minimum value in the set

## What is Mean, Median, Mode and Range?

Mean, Median, Mode and Range are measure of central tendency in statistical values of the data.It is defined as below
Mean is the sum of all the values divided by the number of values
$Mean = \frac {x_1 + x_2 + x_3 +..+x_n}{n}$
Median is the middle-value in the list of numbers which is derived by sorting the list by ascending order and then select the middle one.

Mode is the value which is repeated maximum times.

Range is the difference of maximum and minimum value in the set

Example of Few questions where you can use this formula
Question 1
Find the Mean, Median, Mode and Range of 1,3,3,4,5,5,6,2,3,4
Solution
Lets first arrange the dataset in ascending order
Ascending order will be
1,2,3,3,3,4,4,5,5,6
Now Mean is calculated as
$Mean = \frac {x_1 + x_2 + x_3 +..+x_n}{n}$
$Mean = \frac { 1 + 2 + 3 + 3 + 3+ 4 + 4 + 5 + 5 + 6}{10} = 3.6$
Now Mode is the value which is repeated maximum times.So mode is 3
Now for median, Since the data count is even, Median will be given by average value of n/2 and n/2 + 1 i,e 5th and 6th number
$Median =\frac { 3 + 4}{2} = 3.5$
Range is difference between max and min
Range = 6 -1 = 5

Question 2
Find the Mean of 164,156,155,145,106,189,211
Solution
Mean is calculated as
$Mean = \frac {x_1 + x_2 + x_3 +..+x_n}{n}$
$Mean = \frac { 164 + 156 + 155 + 145 + 106+ 189 }{6} = 152.5$

Question 3
Find the Median of 11,10, 11, 12, 13,13, 12, 11, 15
Solution
Lets first arrange the dataset in ascending order
Ascending order will be
10,11,11,11,12,12,13,13,15
Now for median, Since the data count is odd,Median will be given by middle number
i.e 12

## How Mean, Median, Mode and Range Calculators works

• First the data is arranged in ascending order
• Now mean is calculated using the formula
$Mean = \frac {x_1 + x_2 + x_3 +..+x_n}{n}$
• Now if the number of values are Odd, Median is calculated as the Middle value in the ascending array
• If the numbers of values are even, then median is the average value of n/2 and n/2 + 1 values in the array
• Mode is value in data which is repeated maximum times.
• Range is simply calculated using the first and last value in the ascending array