# 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).

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