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 using 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, but there is one main difference.

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

**Example: **

The table below 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 highest 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 frequency.

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 height 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:

Let's have a go at some questions.