4.1 Tables, Charts, Gauges & Multi-Step Data Questions

Tables, charts, gauges and multi-step data questions

Read the frame before the numbers

A data display answers only the question defined by its labels. Before calculating, inspect:

1. title and population;
2. row and column headings;
3. unit and time period;
4. legend or colour key;
5. axis origin, interval, and any break;
6. whether figures are counts, rates, percentages, averages, or cumulative totals;
7. footnotes and exclusions.

If a table reports “minutes per response” and another column reports “number of responses,” adding the columns is meaningless. If a chart uses thousands of dollars, a plotted value of 35 means $35,000, not $35.

Locate by coordinates

For a table, verbalise the lookup: “Tuesday row, Site C column, percentage unit.” Trace the row and column with a finger or cursor if permitted. Many errors come from reading an adjacent cell correctly.

For multiple tables, verify that the populations match. A monthly total and a weekday-only average may not be directly comparable. If the question asks for a combined value, identify whether categories overlap; adding overlapping groups double-counts members.

Bar and line charts

Bar charts compare magnitudes. Check whether bars begin at zero. A truncated axis can make a small difference look dramatic. Use the numeric scale, not the apparent length alone.

Line charts usually show change over an ordered dimension such as time. A rising line means the plotted value increases, not necessarily that its rate of increase accelerates. Acceleration would require the slope itself to become steeper.

For change between periods:

• absolute change = later − earlier;
• percentage change = (later − earlier) ÷ earlier × 100%;
• average change per interval = total change ÷ number of intervals.

From January to April there are three intervals: January–February, February–March, and March–April. Dividing by four data points is a common error.

Pie charts and percentages

A pie chart partitions a whole. The shares should total 100%, subject to rounding. To turn a share into a count, multiply the total by the decimal percentage.

If 18% of 450 cases belong to a category, the count is 0.18 × 450 = 81. If two sectors are combined, add percentages only when they are disjoint parts of the same whole.

Gauges and scales

Determine the value per minor division. If labelled marks run from 40 to 60 with four equal spaces, each space represents 5, not 4. Count spaces, not tick marks.

If a pointer lies between divisions, decide whether the question expects interpolation or the nearest marked value. Do not claim greater precision than the display supports. A gauge with 5-unit divisions cannot justify 47.326.

Interpolation

Linear interpolation assumes equal movement between known points. If a marker lies three quarters of the way from 80 to 100, estimate 80 + 0.75 × 20 = 95. Use interpolation only when the scale is linear; logarithmic or categorical axes require different reading.

Averages and weighted data

The mean is total divided by count. The median is the middle ordered value, and the mode is the most frequent value. A weighted mean is:

sum(value × frequency) ÷ sum(frequency).

Suppose Site A averages 6 minutes over 10 events and Site B averages 9 minutes over 30 events. The combined mean is:

(6 × 10 + 9 × 30) ÷ 40 = 330 ÷ 40 = 8.25 minutes.

The simple mean of 6 and 9 is 7.5, but it wrongly gives the two sites equal influence despite different event counts.

Cumulative information

A cumulative graph gives the total up to a point. The number within an interval is the later cumulative total minus the earlier cumulative total. If the total is 120 by noon and 185 by 14:00, then 65 occurred between noon and 14:00.

Percentiles on a cumulative curve identify the value below which a stated percentage falls. They are not percentages of the measurement itself.

Multi-step workflow

For “What percentage of all events across two months occurred at Site B?”:

1. extract Site B counts for both months;
2. add them for the numerator;
3. add all sites and both months for the denominator;
4. divide numerator by denominator;
5. multiply by 100 and round as directed.

Write the numerator and denominator in words before inserting numbers. This prevents using one month’s total against two months of Site B data.

Sanity checks

Compare your answer with the display. A category percentage cannot exceed 100%. A weighted mean must lie between the smallest and largest contributing values. A cumulative series cannot fall unless the definition permits removals or corrections. If the chart shows a small change but your result is a tenfold increase, recheck units, axis scale, and decimal placement.