Here you’ll learn how to find the median of grouped data. In this case, you find the median by reading off a graph or through calculation. Here’s the procedure for both methods.
To find the median in a set of grouped data, you need to draw the graph representing the relative cumulative frequency. This is how you do it:
Rule
For grouped data, you can assume the values are evenly distributed inside each interval. That’s why you can find the median of grouped data by reading off the graph when the relative cumulative frequency is known.
Rule
You find the median where the relative cumulative frequency passes , or %.
When you need to find the median through calculation, you have to find the expression for a line between two points. These points are taken from the interval where the relative cumulative frequency passes %, and the interval before it. Here’s how to do it:
Rule
Example 1
Below you can see a table showing the relative cumulative frequency of the weight of newborn children.
Weight | Relative Cumulative Frequency |
| % |
| % |
| % |
| % |
| % |
| % |
| % |
From the table, you can see that the relative cumulative frequency passes % in the interval . That means you have , , and . That gives us the points and .
Calculate by using these values in the formula
Calculate by inserting the point and the value of into :
You then get the expression for the line:
Set it equal to (as our numbers are percentages) and solve for :
You’ve found the median of the given birth weights to be kg.