Bar Charts and Histograms

Bar Charts

Bar charts are used to display categorical data, which means data sorted into distinct groups or categories, such as types of land use, transport modes, or population groups. Each category is represented by a bar.

• Bars show the frequency (how many) or amount for each category.
• All bars have equal width to ensure fair comparison.
• There are clear gaps between bars to show that categories are separate and not continuous.
• The height of each bar corresponds to the value it represents.

Bar charts are ideal for comparing different groups, such as the number of visitors to different UK national parks or the types of transport used by commuters in a city.

For instance, if a bar chart shows the number of tourists visiting four UK cities in millions: London ($9\,\mathrm{million}$), Edinburgh ($3\,\mathrm{million}$), Manchester ($2\,\mathrm{million}$), and Cardiff ($1\,\mathrm{million}$), the bars for each city will be equally wide, spaced apart, and their heights will reflect these numbers.

Histograms

Histograms are used for displaying continuous data, which means data measured over intervals, such as temperature ranges, rainfall amounts, or age groups.

• Bars represent frequency density, not just frequency. Frequency density is calculated as:

Frequency density = $\frac{\text{Frequency}}{\text{Class width}}$

• Bars in histograms touch each other to show the data is continuous.
• The area of each bar (height $\times$ width) is proportional to the frequency of data in that interval.
• The width of bars corresponds to the class interval size.

Histograms are useful for showing distributions of data, such as rainfall in $\mathrm{mm}$ over different ranges of days or temperature ranges in a UK city over a month.

For example, if rainfall is recorded in intervals of 0–5 $\mathrm{mm}$, 5–10 $\mathrm{mm}$, and 10–15 $\mathrm{mm}$, and the frequencies are 4, 8, and 6 days respectively, the bars will have widths of 5 $\mathrm{mm}$ intervals and heights calculated from frequency density.

Interpreting Bar Charts and Histograms

When analysing bar charts and histograms, you should:

• Identify trends and patterns: Look for which categories or intervals have the highest or lowest values.
• Compare categories or intervals: See how values differ between groups or ranges.
• Recognise skewness and distribution shape: For histograms, note if the data is symmetrical, skewed left or right, or has multiple peaks.

For example, a histogram showing temperature ranges might be skewed to the right if most days are cool but a few are very hot.

Learning example: Calculating frequency density for a histogram

Suppose rainfall data is grouped into intervals with different widths:

• 0–2 $\mathrm{mm}$: 6 days
• 2–5 $\mathrm{mm}$: 9 days
• 5–10 $\mathrm{mm}$: 15 days

Calculate frequency density for each interval:

• 0–2 $\mathrm{mm}$: width = 2, frequency = 6 $\rightarrow$ frequency density = $\frac{6}{2} = 3$
• 2–5 $\mathrm{mm}$: width = 3, frequency = 9 $\rightarrow$ frequency density = $\frac{9}{3} = 3$
• 5–10 $\mathrm{mm}$: width = 5, frequency = 15 $\rightarrow$ frequency density = $\frac{15}{5} = 3$

All bars would have heights of 3, but different widths, so the area of each bar corresponds to the frequency.