Statistics - Frequency Tables
A frequency table is a way to present data. The data are counted and ordered to summarize larger sets of data.
With a frequency table you can analyze the way the data is distributed across different values.
Frequency Tables
Frequency means the number of times a value appears in the data. A table can quickly show us how many times each value appears.
If the data has many different values, it is easier to use intervals of values to present them in a table.
Here is the age of the 934 Nobel Prize winners up until the year 2020. In the table each row is an age interval of 10 years.
| Age Interval | Frequency |
|---|---|
| 10-19 | 1 |
| 20-29 | 2 |
| 30-39 | 48 |
| 40-49 | 158 |
| 50-59 | 236 |
| 60-69 | 262 |
| 70-79 | 174 |
| 80-89 | 50 |
| 90-99 | 3 |
We can see that there is only one winner from ages 10 to 19. And that the highest number of winners are in their 60s.
Note: The intervals for the values are also called 'bins'.
Relative Frequency Tables
Relative frequency means the number of times a value appears in the data compared to the total amount. A percentage is a relative frequency.
Here are the relative frequencies of ages of Noble Prize winners. Now, all the frequencies are divided by the total (934) to give percentages.
| Age Interval | Relative Frequency |
|---|---|
| 10-19 | 0.11% |
| 20-29 | 0.21% |
| 30-39 | 5.14% |
| 40-49 | 16.92% |
| 50-59 | 25.27% |
| 60-69 | 28.05% |
| 70-79 | 18.63% |
| 80-89 | 5.35% |
| 90-99 | 0.32% |
Cumulative Frequency Tables
Cumulative frequency counts up to a particular value.
Here are the cumulative frequencies of ages of Nobel Prize winners. Now, we can see how many winners have been younger than a certain age.
| Age | Cumulative Frequency |
|---|---|
| Younger than 20 | 1 |
| Younger than 30 | 3 |
| Younger than 40 | 51 |
| Younger than 50 | 209 |
| Younger than 60 | 445 |
| Younger than 70 | 707 |
| Younger than 80 | 881 |
| Younger than 90 | 931 |
| Younger than 100 | 934 |
Cumulative frequency tables can also be made with relative frequencies (percentages).