SPI Mathematics · Free notes

Data Interpretation: SPI Mathematics

Data Interpretation has 6 questions in the SPI bank, all EASY and all from the LWS mock tests, so none is from the 2022 paper. Each one reads a single simple chart: the key of a pictograph, the axes of a bar graph, or the share, angle and amount of a pie chart sector. One multiplication or division settles each, so the marks are lost only by reading the chart the wrong way round, such as taking a percentage for an angle.

The handout has every subtopic, worked example, formula and trap with answers shown. The formula sheet is the chapter’s formulas and traps alone, on one page.

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Subtopic notes

Pictographs, Bar Graphs and Pie Charts
6 questions
A pictograph counts with symbols, a bar graph compares with bar heights, and a pie chart shares out 360° in proportion to the parts of a whole.

Formula & revision sheet

2 formulas · 1 reference tables · 7 gotchas across all subtopics — the exam-eve cheat-sheet

Pictographs, Bar Graphs and Pie Charts

Formulas (2)

Reading a pictograph · Pictograph value $\text{value} = \text{number of symbols} \times \text{value of one symbol}$
Pie chart shares, angles and amounts · Pie chart $\text{central angle} = \frac{\text{part}}{\text{whole}} \times 360^\circ \qquad \text{amount} = \frac{\text{angle}}{360^\circ} \times \text{whole}$

Reference tables (1)

The parts of a bar graph6 rows

Part of a bar graph	What it shows
x-axis (horizontal)	The categories being compared, such as years, subjects or cities
y-axis (vertical)	The values, marked on an even scale
Height of a bar	The value of that category
Gaps between bars	Equal gaps and equal widths, because the categories are separate
Scale	How much one unit of height stands for, such as 1 cm for 5 students
Horizontal bar graph	The bars lie sideways: categories on the y-axis, values on the x-axis Only the sideways graph swaps the axes. The usual bar graph has its categories on the x-axis.

Value of a bar = its height × what one unit of height stands for.

Watch out for (7)

Using the part symbol's value as the key
→ Reading a pictograph
Counting a half symbol as a full one
→ Reading a pictograph
Mixing up a bar graph and a histogram
→ The parts of a bar graph
Reading the height without the scale
→ The parts of a bar graph
Taking a percentage as the angle
→ Pie chart shares, angles and amounts
Dividing an angle by 100
→ Pie chart shares, angles and amounts
Forgetting the share that is not printed
→ Pie chart shares, angles and amounts

Question weightage by concept

3 concepts · 6 questions — where the marks actually sit, so you know what to drill first

Pictographs, Bar Graphs and Pie Charts6 questions · 100%

Concept	Qs	Share
Pie chart shares, angles and amounts	3	50%
Reading a pictograph	2	33%
The parts of a bar graph	1	17%

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