Frequency tables: finding averages
In a nutshell
Just like for sets of values, the mean, median, mode and range can be found from frequency tables too. The only difference is that these averages might refer to a category, rather than an individual number.
PROCEDURE
Mean | Create a new column: 'number × frequency' and calculate these values. Next, find the sum of all these values, then divide this number by the total frequency. |
Median | Identify the category containing the middle value: use 2n+1 where n is the total frequency to find the middle position. |
Mode | Identify the category with the highest frequency. |
Range | Calculate the difference between the highest and lowest in the 'number of' column. |
Example
This frequency table shows the number of siblings pupils in a class of 23 have:
Number of siblings | Frequency |
0 | |
| |
| |
| |
| |
Find the mean, median, range and mode.
1. Mean:
Add the third column to the table.
Number of siblings × frequency |
|
1×12=12 |
|
|
|
Use the formula:
total frequencysum of ’number×frequency’ column=6+12+3+212+6+6=2324=1.043 (to 3 d.p)
Note: The total number of students was given in the question here, but often you will need to calculate it yourself.
2. Median:
Identify the middle position.
2(n+1)=2(23+1)=12
The median is the category containing the 12th value cumulatively: 1
3. Mode:
Identify the category with the highest frequency.
1
4. Range:
Work out the difference between the highest and lowest number of siblings.
3−0=3
Note: 4 is not used here as there is no one with 4 siblings.