# Statistics » Frequency and frequency table

## Contents

1. What is a frequency?
2. What is a frequency table?
3. How do you make a frequency table?
4. How do you make a frequency table with grouped data / distribution in classes?
5. What is a cumulative frequency table?

## 1. What is a frequency?

The number of times a certain value appears in a row/set of data is called the frequency. Frequency is a better word for number.

## 2. What is a frequency table?

A table, in which the frequencies of a row of data can be found is called a frequency table. Often the tables are vertically, so with two columns and multiple rows. The values are on the left and the frequencies on the right.

## 3. How do you make frequency table?

Find the lowest value and highest value of your row of numbers.
These numbers you can write in the left column.
In the right column you write the frequencies.

If you find this convenient, you can put a column in the middle so you can tally.

Example
For a test the following marks are scored:
7,  6,  9,  4,  5,  5,  6,  6,  7,  7,  7,  9,  4,  5,  5,  6,  7,  6,  6,  9,  9,  4

Make a frequency table for this data.

 mark frequency 4 3 5 4 6 6 7 5 8 0 9 4

(Note: It is not necessary to have the row 8 | 0)

## 4. How do you make a frequency table with grouped data / distribution in classes?

With a row of values where all the values are different, a normal frequency table will be very long and will only have frequencies of 1 or 2.
You can choose to make a stem-and-leaf diagram or group the data, sometimes called distribution in classes.

You will group the data in classes. Classes can also be called bins or intervals.
You write down the frequency of these classes.
A class is always from … to … .
Take, for example, class 6.0 to 7.0.
Values that can be in this class are: 6.0, 6.4, 6.9, 6.15 or 6.99.
7.0 is not in this class, it will be in class 7.0 to 8.0.
Sometimes the notation '6.0 – < 7.0' is used to show this.

You can choose the classes yourself. Make sure you have about 5 or 6 classes.
(3 classes is really not enough, you can choose for example a class from 5.0 to 5.5)

Example
Given are the following lengths in cm:
0.3   4.6   3.8   4.9   1.5   0.9   1.0   1.6
2.4   2.7   3.6   0.4   1.3   4.4   3.1   4.0

Make a distribution in classes of this data.

 length in cm frequency 0.0 to 1.0 1.0 to 2.0 2.0 to 3.0 3.0 to 4.0 4.0 to 5.0 3  4  2  3  4

Note 1: The value 1.0 is in class 1.0 to 2.0.
Note 2: Check mode, median and mean to learn how you can find the mode and estimate the mean of a distribution in classes.

## 5. What is a cumulative frequency table?

A cumulative frequency of a value is the sum of all the frequencies leading up to this value from the lowest value.

Example
In the table below are the results of a expiration date test of packaged lettuce.
They test 30 bags on how long it takes until they go bad/are rotten.

 day cumulative frequency 6 7 8 9 10 3  10  15  23  30

Note: Because it is a cumulative frequency, on day 7 there is a total of 10 bags that went bad. This is including the 3 bags that went bad on day 6. On day 10 all 30 bags have gone bad.

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