Civil Service Numerical Reasoning Test Data Interpretation: Charts and Graphs Syllabus

With multiple lines on one graph, how do you find the gap (difference) between two series at a specific $x$ value?

Read each line's $y$ value at that $x$, then subtract the smaller from the larger; the largest gap occurs where the vertical distance between the lines is greatest.

In a pie chart, what fraction of the whole does a full circle ($360^{\circ}$) represent?

The full $360^{\circ}$ represents the entire data set, i.e. $100\%$ or the whole total.

How do you convert a pie-chart sector angle into a percentage of the total?

$\text{percentage} = \frac{\text{angle}}{360^{\circ}} \times 100\%$.

How do you convert a percentage share into a pie-chart sector angle?

$\text{angle} = \frac{\text{percentage}}{100} \times 360^{\circ}$.

A sector of a pie chart has an angle of $90^{\circ}$. What percentage and fraction of the total does it represent?

$\frac{90}{360} = \frac{1}{4} = 25\%$ of the total.

If a pie chart represents a total of $800$ people and one sector is $45^{\circ}$, how many people does that sector represent?

$\frac{45}{360} \times 800 = \frac{1}{8} \times 800 = 100$ people.

How do you find the value represented by a pie sector given its percentage and the overall total?

$\text{value} = \frac{\text{percentage}}{100} \times \text{total}$ (or equivalently $\frac{\text{angle}}{360^{\circ}} \times \text{total}$).

When comparing two pie charts, why can equal-sized sectors represent different absolute values?

Because each pie's sectors are percentages of its own total; equal percentage shares give different absolute values when the two totals differ. Always multiply the share by each chart's own total.

When comparing two pie charts, what must you check before concluding that a larger sector means a larger absolute quantity?

Check whether the two charts represent the same total. If the totals differ, a smaller percentage of a larger total can exceed a larger percentage of a smaller total.

Two pie charts show the same category at $20\%$ of $500$ and $15\%$ of $800$. Which has the larger absolute value?

First: $0.20 \times 500 = 100$. Second: $0.15 \times 800 = 120$. The second is larger despite the smaller percentage.

How do you combine a pie chart percentage with a separate figure given in a table or text?

Apply the pie's percentage to the relevant total taken from the other source: $\text{value} = \frac{\text{pie percentage}}{100} \times \text{total from table/text}$.

A pie chart shows $30\%$ of staff are part-time, and a table states the company has $1{,}200$ staff. How many are part-time?

$0.30 \times 1200 = 360$ part-time staff.

To find what percentage a pie sub-group is of a grand total across multiple sources, what two steps are needed?

First convert the pie share to an absolute value using its own total, then divide that value by the grand total and multiply by $100$: $\frac{\text{absolute value}}{\text{grand total}} \times 100\%$.

What does a scatter plot display, and what is each point?

A scatter plot displays the relationship between two continuous variables; each point represents one observation with coordinates $(x, y)$ giving its values on the two variables.

What does positive correlation look like on a scatter plot?

As $x$ increases, $y$ tends to increase; the points slope upward from lower-left to upper-right.

What does negative correlation look like on a scatter plot?

As $x$ increases, $y$ tends to decrease; the points slope downward from upper-left to lower-right.

What does it mean if a scatter plot shows no correlation?

There is no clear linear pattern between the variables; the points are scattered randomly with no consistent upward or downward trend.

How do you judge the strength of a correlation from a scatter plot?

The more tightly the points cluster around a straight line, the stronger the correlation; the more widely they are spread, the weaker it is.

What is a line of best fit on a scatter plot, and what is it used for?

A straight line drawn to pass as close as possible through the centre of the data points; it summarises the trend and can be used to predict $y$ for a given $x$.

What important caution applies when interpreting correlation in a scatter plot?

Correlation does not imply causation — a relationship between two variables does not prove that one causes the other; a third factor may be responsible.

What is an outlier on a scatter plot?

A point that lies far away from the general pattern of the other points, not following the overall trend.

In a combination chart with bars and a line, what is the typical purpose of using two different chart types together?

To display two related but differently-scaled quantities at once — e.g. bars for absolute amounts (like revenue) and a line for a rate or trend (like percentage growth) — on a shared horizontal axis.

In a combination bar-and-line chart with two vertical axes, how do you read each series correctly?

Read the bars against the axis on one side (usually the left) and the line against the axis on the other side (usually the right), matching each series to its own scale via the legend.

Why is it a common error to compare the height of a bar directly with the height of a line in a dual-axis combination chart?

Because the bars and line are plotted on different scales; equal pixel heights do not mean equal values, so you must read each series against its own axis.

What are common ways a chart can be designed to create a visual misreading of the data?

A vertical axis that does not start at zero (exaggerating differences), a truncated or non-linear scale, inconsistent intervals, 3D effects distorting sizes, or unequal bar widths.

Why does a bar chart with a $y$-axis that starts above zero risk misleading the reader?

Truncating the axis exaggerates the visual difference between bars, making small differences look large; always check the axis baseline before judging relative sizes.

What should you always check on the axes before reading values from any chart?

Check the units, the scale interval between gridlines, where the axis starts (zero or truncated), and whether the scale is linear, to avoid misreading values.

How can a 3D pie chart visually distort the perception of sector sizes?

The perspective tilt makes sectors at the front appear larger and those at the back appear smaller than their true angles, so rely on the labelled percentages or angles rather than apparent area.

On a graph, why must you check the units of the axis labels before performing a calculation?

Values may be in thousands, millions, or percentages; misreading the units (e.g. treating '$£m$' as '$£$') leads to answers wrong by orders of magnitude. Always read the units and any multiplier note.

What is the safest first step before answering any data-interpretation question on a chart?

Read the title, axis labels, units, legend, and any footnotes to understand exactly what the chart shows and on what scale, before reading off or calculating any values.