Choosing the Right Statistical Diagram GCSE: Bar Chart, Histogram and More

What determines which diagram to use?

Two questions narrow your choice almost every time:

1. What type of data do you have?

• Categorical data — named groups with no natural order (e.g. favourite colour, type of transport).
• Discrete data — whole-number counts (e.g. number of siblings, shoe size).
• Continuous data — measured values that can take any value in a range (e.g. height, time, mass).
• Bivariate data — two numerical variables recorded together (e.g. height and arm span).

2. What is the diagram for?

• Showing how data is distributed across categories or groups.
• Comparing two or more data sets.
• Looking for a relationship or trend between two variables.
• Showing proportions of a whole.

Answer both questions, then match your answer to the table below.

Which diagram suits categorical or discrete data?

Bar charts — the default choice for categorical or discrete data. Each bar represents one category; bars are separated by a gap to show that categories are distinct (not continuous). Bar charts can be drawn vertically or horizontally. Use a comparative (dual) bar chart to compare two groups side by side.

Pie charts — best when you want to show each category as a proportion of the whole. The whole circle represents 100 %; each sector represents one category. Pie charts are less useful for comparing totals or reading exact frequencies.

Key distinction: a bar chart compares sizes directly; a pie chart shows each category's share of the whole. If you need to do both, use a bar chart.

When do you use a histogram?

A histogram is for continuous data grouped into class intervals. Its key features:

• The horizontal axis is a continuous scale — no gaps between bars.
• The vertical axis shows frequency density, not frequency: frequency density = frequency ÷ class width.
• Bars of unequal width are allowed (and common in GCSE questions).

Do not use a histogram for categorical or discrete data — the continuous scale would be meaningless. Do not confuse a histogram with a bar chart: bar charts have gaps and equal widths; histograms have no gaps and can have unequal widths.

When to choose a histogram: continuous data, especially with unequal class intervals or a large range (e.g. reaction times, lengths, weights).

Worked example: A survey records journey times in minutes: 0 < t ≤ 10 (12 people), 10 < t ≤ 20 (18), 20 < t ≤ 40 (20), 40 < t ≤ 60 (10).

Frequency densities: 12÷10 = 1.2, 18÷10 = 1.8, 20÷20 = 1.0, 10÷20 = 0.5.

These are plotted as bars of width 10, 10, 20, 20 respectively. The varying widths make a histogram necessary — a bar chart would misrepresent the data.

When do you use a scatter graph?

A scatter graph plots two numerical variables, one on each axis, as individual points. It is the correct choice when you want to explore whether there is a relationship (correlation) between two measured quantities.

After plotting, draw a line of best fit (by eye through the point of mean values) if a linear trend is visible, and describe the correlation: positive, negative, or none.

Examples where a scatter graph is correct:

• Height vs shoe size for a group of students.
• Hours of revision vs exam mark.
• Temperature vs ice cream sales.

Important: a scatter graph shows correlation only — it does not prove causation. State this in your answer if asked to interpret the data.

When should you use a box plot?

A box plot (box-and-whisker diagram) displays five summary statistics: minimum, lower quartile (Q1), median (Q2), upper quartile (Q3), and maximum. Its main use at GCSE is comparing two distributions on the same scale.

From a box plot you can read:

• Median — central tendency.
• Interquartile range (IQR = Q3 − Q1) — spread of the middle 50 %.
• Range — overall spread.
• Skewness — whether the median is closer to Q1 (positive skew) or Q3 (negative skew).

Choose a box plot when the question asks you to compare the spread or consistency of two data sets, or when you need to describe the shape (skewness) of a distribution.

What is a frequency polygon used for?

A frequency polygon plots the midpoint of each class interval against its frequency, then joins the points with straight lines. It is best for comparing two or more continuous distributions on the same axes, because two frequency polygons can be overlaid without confusion — two histograms on the same axes would overlap messily.

Use a frequency polygon instead of a histogram when you need to compare distributions. Use it instead of a bar chart when your data is continuous.

Quick reference: which diagram to choose

Frequently asked questions

Can I use a bar chart for continuous data?

Technically no — a bar chart implies distinct categories (shown by the gaps). For continuous data, a histogram is correct. In practice, some GCSE questions accept a bar chart for grouped continuous data with equal widths, but if class widths are unequal, a histogram with frequency density is always required.

What is the difference between a histogram and a frequency polygon?

Both display continuous grouped data. A histogram uses bars (area = frequency); a frequency polygon uses lines joining midpoints. The main advantage of a frequency polygon is that two or more distributions can be drawn on the same axes without one obscuring the other. A histogram shows individual class frequencies more clearly.

Why can't I use a pie chart to compare two groups?

A pie chart only shows proportions within one group. If you draw two separate pie charts, you can compare proportions but not totals — the charts look similar even if one group is ten times larger. Use a comparative bar chart to compare both frequency and proportion simultaneously.

Does it matter which diagram I choose if I draw it correctly?

Yes — marks are awarded for selecting the appropriate diagram as well as for accuracy. A histogram drawn correctly but used for categorical data would lose the selection mark. If the question says "draw a suitable diagram," state which type you chose and why before drawing it.

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