## Plotting a Data Frequency Distribution Histogram

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### Explanation

What is a Frequency Distribution Histogram?

Plotting data is the best way to start to understand it. On this page, we will look at ways of plotting data from a single variable.

Plotting the actual values of a single variable is not always a good way of visualising that data. A useful approach is to count how often each value occurs in the data and plot those counts, which are called frequencies. These frequencies are plotted in a bar chart, known as a histogram. Histograms show how often each value occurs in a sample of data or, for continuous variables, how often values fall into different small ranges. There is an extra help topic below that explains the difference between discrete and continuous values.

Histograms are easy to interpret. Each value that occurs in the data has its own vertical bar in the chart. The height of the bar tells you how many data points in the sample took that value. Here is an example showing the number of children that a sample of 100 people have.

You can immediately see that the number of children runs from 0 to 4 (along the horizontal axis) and that the most common number of children is 2. 42 people have 2 children in this sample.

### Exploration

Use this game to explore the relationship between raw data and the frequency histogram of that data. Enter a whole number from 1 to 3 in each box, click 'Go', and look at the histogram that is formed. Note that you are entering raw data, but the chart is showing the frequency histogram, not the data.
Try and answer the following questions:
• What is plotted along the horizontal (x) axis?
• What is plotted up the vertical (y) axis?
Note that the numbers themselves are not getting plotted (1,2,3). It is how many times they appear that dictates the height of the bars

Try and make the following shapes:

• All bars the same height
• Two high bars and one very low
• Two empty bars and one at full height
• An upward slope so that the third bar is higher than the second, which is higher than the first.

Does the order in which you enter values make a difference to the histogram?

( You need to enable Java to see this applet. )

### Application

Let's look at cost, which is plotted below. It is a discrete variable, which means it can only have values that are whole numbers. Each different value that appears in the data has a frequency bar of its own.

Look at the histogram above and answer the questions below.
 What is the lowest value of cost? What is the highest value of cost? How many different values does cost take? What is the most common value taken by cost? How many times does that value appear?

Now let's look at no. Apps

Compare the histograms for the two different variables to answer the questions below.
Which variable has the lowest value?
Which variable has the highest value?

 Introduction to Your Study | Central Tendency