Comparing histograms and bar charts Revision Card

AI generatedStatisticsGCSE Higher / IGCSE Extended

Comparing histograms and bar charts.

A histogram uses a numerical horizontal scale and bar area to represent frequency.
When widths differ, bar height is frequency density, so compare areas.
A standard bar chart uses height for frequency and equal-width separated bars for categories.

Example 1

A histogram has a width-5 bar of height 6 and a width-10 bar of height 4. Which class has the larger frequency? Explain how reading a bar chart would differ.

First frequency

Histogram frequency is the bar area: width × density.

Second frequency

Unequal widths mean height alone cannot compare frequencies.

The second class has the larger frequency. In a standard bar chart, frequency is read from height; equal-width bars represent separate categories.

Example 2

A histogram has a width-10 bar of height 3 and a width-5 bar of height 6. Compare their frequencies. Explain how reading a bar chart would differ.

First frequency

Histogram frequency is the bar area: width × density.

Second frequency

Unequal widths mean height alone cannot compare frequencies.

The frequencies are equal. In a standard bar chart, frequency is read from height; equal-width bars represent separate categories.

Your turn

Question 1

A histogram has a width-4 bar of height 5 and a width-8 bar of height 3. Which class has the larger frequency? Explain how reading a bar chart would differ.

Check answer

First frequency

Histogram frequency is the bar area: width × density.

Second frequency

Unequal widths mean height alone cannot compare frequencies.

The second class has the larger frequency. In a standard bar chart, frequency is read from height; equal-width bars represent separate categories.

Question 2

A histogram has a width-2 bar of height 7 and a width-6 bar of height 3. Compare their frequencies. Explain how reading a bar chart would differ.

Check answer

First frequency

Histogram frequency is the bar area: width × density.

Second frequency

Unequal widths mean height alone cannot compare frequencies.

The second class has the larger frequency. In a standard bar chart, frequency is read from height; equal-width bars represent separate categories.

Question 3

A histogram has a width-8 bar of height 2 and a width-4 bar of height 5. Which class has the larger frequency? Explain how reading a bar chart would differ.

Check answer

First frequency

Histogram frequency is the bar area: width × density.

Second frequency

Unequal widths mean height alone cannot compare frequencies.

The second class has the larger frequency. In a standard bar chart, frequency is read from height; equal-width bars represent separate categories.

Question 4

A histogram has a width-5 bar of height 8 and a width-10 bar of height 4. Compare their frequencies. Explain how reading a bar chart would differ.

Check answer

First frequency

Histogram frequency is the bar area: width × density.

Second frequency

Unequal widths mean height alone cannot compare frequencies.

The frequencies are equal. In a standard bar chart, frequency is read from height; equal-width bars represent separate categories.

Question 5

A histogram has a width-10 bar of height 5 and a width-5 bar of height 7. Which class has the larger frequency? Explain how reading a bar chart would differ.

Check answer

First frequency

Histogram frequency is the bar area: width × density.

Second frequency

Unequal widths mean height alone cannot compare frequencies.

The first class has the larger frequency. In a standard bar chart, frequency is read from height; equal-width bars represent separate categories.