HTML tutorial
CSS3 tutorial
Bootstrap tutorial
JavaScript tutorial
JQuery tutorial
AngularJS tutorial
React tutorial
NodeJS tutorial
PHP tutorial
Python tutorial
Python3 tutorial
Django tutorial
Linux tutorial
Docker tutorial
Ruby tutorial
Java tutorial
C tutorial
C ++ tutorial
Perl tutorial
JSP tutorial
Lua tutorial
Scala tutorial
Go tutorial
ASP.NET tutorial
C # tutorial
The median is a type of average value, which describes where the center of the data is located
The median is the middle value in a data set ordered from low to high.
The median can only be calculated for numerical variables.
The formula for finding the middle value is:
\( \displaystyle \frac{n + 1}{2} \)
Where \(n\) is the total number of observations.
If the total number of observations is an odd number, the formula gives a whole number and the value of this observation is the median.
13, 21, 21, 40, 48, 55, 72
Here, there are 7 total observations, so the median is the 4th value:
\( \displaystyle \frac{7 + 1}{2} = \frac{8}{2} = 4 \)
The 4th value in the ordered list is 40, so that is the median.
If the total number of observations is an even number, the formula gives a decimal number between two observations.
13, 21, 21, 40, 42, 48, 55, 72
Here, there are 8 total observations, so the median is between the 4th and 5th values:
\( \displaystyle \frac{8 + 1}{2} = \frac{9}{2} = 4.5 \)
The 4th and 5th values in the ordered list is 40 and 42, so the median is the mean of these two values. That is, the sum of those two values divided by 2:
\( \displaystyle \frac{40+42}{2} = \frac{82}{2} = \underline{41} \)
Note: It is important that the numbers are ordered before you can find the median.
The median can easily be found with many programming languages.
Using software and programming to calculate statistics is more common for bigger sets of data, as finding it manually becomes difficult.
With Python use the NumPy library median()
method to find the median of the values 13, 21, 21, 40, 42, 48, 55, 72:
import numpy
values = [13,21,21,40,42,48,55,72]
x = numpy.median(values)
print(x)
Use the R median()
function to find the median of the values 13, 21, 21, 40, 42, 48, 55, 72:
values <- c(13,21,21,40,42,48,55,72)
median(values)