The class midpoint (also called the class mark) is defined to be the average of the upper and lower values of a given class interval. The use of the class midpoint in a frequency distribution table is that it replaces a range of values with a single value. We can use the class midpoint and the frequency to construct line graph for our data.
How to find Class Midpoint/Class Mark in a Frequency Table?
1) Note down the upper and lower limits for the first class interval.
2) Add the two values and then divide the result by 2, that is, take the average of the upper and lower class boundaries.
3)Repeat the procedure for each class interval and find all class midpoints.
4) An alternative way to find class midpoint is to add half of the class width to the lower class interval.
Let us understand the above procedure by means of a simple example.
Example: Consider the following grouped distribution table giving marks obtained in an exam vs the number of students in a class:
| Class intervals(Marks) | Frequencies(Number of students) |
| 0-10 | 7 |
| 10-20 | 12 |
| 20-30 | 13 |
| 30-40 | 3 |
| 40-50 | 5 |
The class mark/class midpoint for the first interval is calculated using the formula,
Class Midpoint=(Upper class boundary+ Lower class boundary)/2 = 0+10/2 = 5.
We similarly calculate the class mark for each class interval and obtain the frequency table as follows,
| Class Marks/Class Midpoint | Frequencies(Number of students) |
| 5 | 7 |
| 15 | 12 |
| 25 | 13 |
| 35 | 3 |
| 45 | 5 |
Note that we could have found the class mark for 0-10 using the alternative way in Step 4 as well,
Class mark = Lower boundary + ½*Class width = 0 + ½*10 = 0+ 5 = 5.
Notice that we will get the same result using this method.
