How do you tabulate data and choose the right chart for categorical and discrete data, including stem-and-leaf and comparative diagrams?
Construct and interpret frequency tables, two-way tables, pictograms, bar charts (including composite and comparative), pie charts and stem-and-leaf diagrams, choosing the correct display for the type of data.
A CCEA GCSE Statistics answer on tabulating and displaying data: frequency and two-way tables, pictograms, bar charts including composite and comparative bar charts, pie charts and stem-and-leaf diagrams, and choosing the right display.
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What this dot point is asking
Once data is collected it must be organised and displayed so the patterns are clear. CCEA expects you to tabulate data in frequency and two-way tables and to construct and interpret the standard displays for categorical and discrete data: pictograms, bar charts (including composite and comparative bar charts), pie charts and stem-and-leaf diagrams. The skill is choosing the display that suits the data and reading values back out of it accurately.
Tables: frequency and two-way
A frequency table lists each value or category with how often it occurs; for discrete data with many values, or for continuous data, values are grouped into classes.
Two-way tables are a frequent early question: complete the missing entries by using the fact that each row and each column adds to its total.
Pictograms and bar charts
A pictogram uses a symbol to represent a fixed number of items, with a clear key (for example, one circle equals 5 people). Part-symbols show fractions of that number, and the key must be stated.
A bar chart displays categorical or discrete data with bars of equal width separated by gaps (the gaps distinguish it from a histogram). Two variations are tested:
- A composite (stacked) bar chart stacks sub-groups within each bar to show how a total splits up.
- A comparative (dual or multiple) bar chart places sub-group bars side by side so two groups can be compared category by category.
The height (or length) of each bar shows the frequency, and the axes must be labelled with a uniform scale.
Pie charts
A pie chart shows how a total divides into proportions, with each category drawn as a sector whose angle is its share of 360 degrees.
To compare two pie charts of different totals, remember each shows proportions, not amounts, so a larger sector means a larger share, not necessarily a larger number.
Stem-and-leaf diagrams
A stem-and-leaf diagram displays the actual data while keeping it ordered.
A back-to-back stem-and-leaf diagram puts one group's leaves on the left and another's on the right of a shared stem, which is ideal for comparing two distributions. Every stem-and-leaf diagram needs a key.
Why this matters
Tables and charts are the representation half of the enquiry cycle, and reading data accurately out of them is tested in both units, including in the Unit 2 case study. Stem-and-leaf diagrams link directly to medians, quartiles and the range, while pie charts test proportional reasoning. Choosing a misleading display, or reading a pie chart as amounts rather than proportions, is exactly the kind of error CCEA asks you to identify and avoid.
Exam-style practice questions
Practice questions written in the style of CCEA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
CCEA-style3 marksIn a survey of 90 people, 36 chose tea, 30 chose coffee and 24 chose juice. Work out the angle for each sector of a pie chart.Show worked answer →
Each person is worth .
Tea: . Coffee: . Juice: .
Check: . One mark for the method (degrees per person or the fraction ), one for two correct angles, one for all three and a total of . A pie chart shows proportions of a whole, so the angles must sum to .
CCEA-style4 marksThe stem-and-leaf diagram shows test marks. Stem 1 | 2 5 8; Stem 2 | 0 3 3 7; Stem 3 | 1 4 (key 1 | 2 means 12). Find the median and the range.Show worked answer →
There are values, listed in order from the diagram: .
Median: the middle value is at position , so the median is . Two marks (one for or locating the middle, one for ).
Range: largest minus smallest . Two marks (one for reading 34 and 12, one for 22). A stem-and-leaf diagram keeps the raw data in order, which makes the median and range quick to read.
Related dot points
- Construct and interpret frequency polygons, histograms with equal and unequal class widths using frequency density, and cumulative frequency curves, and read the median and quartiles from a cumulative frequency curve.
A CCEA GCSE Statistics answer on representing grouped continuous data: frequency polygons, histograms with frequency density and unequal class widths, cumulative frequency tables and curves, and reading the median and quartiles.
- Calculate the mean, median and mode, find a weighted mean and the mean from a frequency or grouped frequency table, identify the modal class, and choose the most appropriate average for the data.
A CCEA GCSE Statistics answer on measures of central tendency: the mean, median and mode, the weighted mean, the mean from frequency and grouped tables, the modal class, and choosing the most appropriate average.
- Find the range, quartiles, interquartile range and percentiles, calculate the standard deviation, identify outliers, and draw and compare box plots of two distributions.
A CCEA GCSE Statistics answer on measures of spread: range, quartiles, interquartile range, percentiles, standard deviation, identifying outliers, and drawing and comparing box plots of two distributions.
- Classify data as qualitative or quantitative, discrete or continuous, primary or secondary, and design good questionnaires, data-collection sheets and surveys that avoid bias and leading questions.
A CCEA GCSE Statistics answer on collecting data: types of data, primary and secondary sources, designing questionnaires and data-collection sheets, leading and biased questions, response classes, and pilot surveys.
- Plot and interpret a time series, calculate moving averages to smooth the data, plot and use a trend line, identify seasonal variation, and use the trend to make predictions.
A CCEA GCSE Statistics answer on time series: plotting a time series, calculating moving averages to smooth fluctuations, plotting a trend line, identifying seasonal variation, and using the trend to predict.
Sources & how we know this
- CCEA GCSE Statistics (2017) specification (2260) — CCEA (2017)