Skip to main content
ScotlandApplications of MathematicsSyllabus dot point

How do you extract and interpret data from tables and statistical diagrams such as bar charts, pie charts, line graphs and stem-and-leaf diagrams?

Extracting and interpreting data from different graphical forms including tables, bar charts, pie charts, line graphs and stem-and-leaf diagrams, and constructing these diagrams from raw data.

A focused answer to the SQA National 5 Applications of Mathematics statistics content on diagrams, covering extracting and interpreting data from tables, bar charts, pie charts, line graphs and stem-and-leaf diagrams, and constructing these diagrams from raw data.

Generated by Claude Opus 4.811 min answer

Reviewed by: AI editorial process; not yet individually human-reviewed

Have a quick question? Jump to the Q&A page

Jump to a section
  1. What this dot point is asking
  2. Reading tables and bar charts
  3. Pie charts
  4. Stem-and-leaf diagrams
  5. Examples in context
  6. Try this

What this dot point is asking

The SQA wants you to extract and interpret data from a range of statistical diagrams, including tables, bar charts, pie charts, line graphs and stem-and-leaf diagrams, and to construct these diagrams from raw data, reading values accurately and drawing sensible conclusions.

Reading tables and bar charts

A table sets out data in rows and columns. To read a value, find the correct row and column and take the entry where they meet. A bar chart shows categories along one axis and frequency up the other, so the height of each bar gives its value against the scale.

Pie charts

A pie chart shows how a total is split between categories, using the angle of each sector. The whole circle is 360∘360^\circ, which represents the whole data set.

Stem-and-leaf diagrams

A stem-and-leaf diagram lists data in order while keeping every value. The stem is the leading digits (often the tens), and each leaf is the final digit, with a key explaining the place value.

Stem-and-leaf diagrams keep the data ordered, which makes them ideal for reading the median and quartiles later in the statistics area. A back-to-back stem-and-leaf diagram puts two data sets on either side of a shared stem, so you can compare them directly: read the left-hand leaves from the stem outwards and the right-hand leaves the usual way. This is a common way to compare two groups, such as the marks of two classes.

Examples in context

Statistical diagrams appear everywhere data is reported: a newspaper bar chart of survey results, a pie chart of a household budget, a line graph of temperature through a day, or a stem-and-leaf diagram of test marks. The SQA tests reading these accurately and drawing a fair conclusion, which feeds directly into comparing data sets and finding averages in the rest of the area.

Try this

Q1. In a pie chart, a category is 13\tfrac{1}{3} of the total. Find its angle. [2 marks]

  • Cue. 13×360=120∘\tfrac{1}{3} \times 360 = 120^\circ.

Q2. A stem-and-leaf row 5∣0  45 \mid 0\;4 (tens and units) represents which values? [1 mark]

  • Cue. 5050 and 5454.

Q3. A pie chart sector of 90∘90^\circ represents what fraction of the total? [2 marks]

  • Cue. 90360=14\dfrac{90}{360} = \dfrac{1}{4}.

Exam-style practice questions

Practice questions written in the style of SQA exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.

SQA N5 Apps style3 marksIn a survey of 9090 people, a pie chart shows that 40%40\% chose tea. Calculate the angle for the tea sector and the number of people who chose tea.
Show worked answer →

A full pie chart is 360∘360^\circ, so each percentage is worth 3.6∘3.6^\circ. The tea sector angle is 40%×360=0.4×360=144∘40\% \times 360 = 0.4 \times 360 = 144^\circ (1 mark). The number of people is 40%40\% of 9090: 0.4×90=360.4 \times 90 = 36 people (1 mark for the method, 1 mark for the answer). Markers reward the sector angle, the percentage of the total, and the correct count. A common slip is finding the angle but forgetting the number of people, or the reverse.

SQA N5 Apps style2 marksA stem-and-leaf diagram has the row 3∣2  5  83 \mid 2\;5\;8 where the stem is tens. List the three data values this row represents.
Show worked answer →

In a stem-and-leaf diagram the stem gives the tens digit and each leaf gives a units digit, so the row 3∣2  5  83 \mid 2\;5\;8 represents 3232, 3535 and 3838 (1 mark for reading the stem correctly, 1 mark for all three values). Markers reward combining the stem with each leaf in turn. A key is always given to show what the stem and leaf mean, so always check it before reading values.

Related dot points

Sources & how we know this