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At the higher level in GCSE maths, you have to be able to make the leap from using a bar chart to represent data to a histogram.

When do I use a histogram? 

Histograms are used when you have continuous data that is grouped.

 

What is the difference between histograms and bar charts.

Both Histograms and Bar Charts are drawn with rectangular bars bu there is one main difference.

In a bar chart, the height is used to represent frequency and in a histogram area is used to represent the frequency.

 

Example: The table gives the heights of a group of boys.

 

Height, h (cm) 151 < h ≤ 153 153 < h ≤ 154 154 < h ≤ 155 155 < h ≤ 159 159 < h ≤ 160
Frequency 120 90 150 240 40

 

Step 1: Find the widths of the bars you need to draw.

This is also called the class width. This can easily be found by subtracting the lowest value of the class from the largest value.

Height, h (cm) 151 < h ≤ 153 153 < h ≤ 154 154 < h ≤ 155 155 < h ≤ 159 159 < h ≤ 160
Frequency 120 90 150 240 40
Class Width 2 1 1 4 1

 

Step 2: Find out how high we need to draw the bars.

We have already said that in a histogram, the area of the bar represents the frquency.

We can say that Frequency = Class Width x Height of the bar

And this can be rearranged into the equation.

Height =
Frequency
Class Width

The correct name of the hight of the bar in a histogram is the Frequency Density, this makes our formula...

Frequency Density =
Frequency
Class Width
Height, h (cm) 151 < h ≤ 153 153 < h ≤ 154 154 < h ≤ 155 155 < h ≤ 159 159 < h ≤ 160
Frequency 120 90 150 240 40
Class Width 2 1 1 4 1
Frequency Density 60 90 150 60 40

 

Step 3: Draw your histogram.

To draw the histogram, we plot the class on the bottom (don't forget to use a continuous scale) and the frequency density up the side.

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