How to Determine the Mean, Median and Mode from Grouped Frequencies
To better explain how to determine the mean, median and mode of grouped frequency data, we will work with common, relatable examples as you can see below-
Ade timed 21 people in the sprint race, to the nearest second:
59, 65, 61, 62, 53, 55, 60, 70, 64, 56, 58, 58, 62, 62, 68, 65, 56, 59, 68, 61, 67
To find the Mean, Ade adds up all the numbers, then divides by how many numbers:
| Mean = | 59+65+61+62+53+55+60+70+64+56+58+58+62+62+68+65+56+59+68+61+67 |
| 21 | |
| = | 61.38095… |
To find the Median Ade places the numbers in value order and finds the middle number.
In this case the median is the 11th number:
53, 55, 56, 56, 58, 58, 59, 59, 60, 61, 61, 62, 62, 62, 64, 65, 65, 67, 68, 68, 70
Median = 61
To find the Mode, or modal value, Ade places the numbers in value order then counts how many of each number. The Mode is the number which appears most often (there can be more than one mode):
53, 55, 56, 56, 58, 58, 59, 59, 60, 61, 61, 62, 62, 62, 64, 65, 65, 67, 68, 68, 70
62 appears three times, more often than the other values, so Mode = 62
Grouped Frequency Table
Alex then makes a Grouped Frequency Table:
| Seconds | Frequency |
|---|---|
| 51 – 55 | 2 |
| 56 – 60 | 7 |
| 61 – 65 | 8 |
| 66 – 70 | 4 |
So 2 runners took between 51 and 55 seconds, 7 took between 56 and 60 seconds, etc
|
Suddenly all the original data gets lost (naughty pup!) Only the Grouped Frequency Table survived … |
… can we help Alex calculate the Mean, Median and Mode from just that table?
Read more below-
