Numerical Reasoning Data Interpretation: Charts, Tables, Ratios and Change
Where numerical reasoning marks are lost: two-source questions, units and scale traps, percentage change against percentage points, ratios and distractors.
The arithmetic on a numerical reasoning test is school level and almost everyone can do it. The marks still go missing, and they go missing before any calculation starts: in the wrong row, the wrong column, the units line nobody read, the second table nobody opened. This article is about reading the stimulus. The arithmetic shortcuts are covered separately, and they only pay off once this part is under control.
Questions that need two sources
Test publishers stopped building single-lookup items years ago, because a single lookup measures eyesight. What they build instead is an item whose answer requires one figure from one exhibit and one from another, and the difficulty is not the combination, it is noticing that a combination is needed at all.
The tell is in the stem, and it is reliable. Look for a noun phrase containing per, as a proportion of, compared with, relative to, or any unit built from two other units.
- Revenue per employee needs a revenue table and a headcount table. The headcount is usually in a different exhibit, often in a different unit, and sometimes only available as a percentage of a total given elsewhere.
- Cost as a share of turnover needs the cost line and the turnover line, and those are routinely split across an income exhibit and a segment exhibit.
- Growth in market share needs the company figure and the market total, for two periods. That is four lookups, and the four are rarely adjacent.
- Anything with a currency conversion needs the rate, which lives in a footnote or a small side table roughly as often as it lives in the main exhibit.
When you see one of those phrases, count the lookups on your fingers before you start. If the count is four and you have only found two places to get them, you have not found the second exhibit yet, and going ahead with two numbers is how you produce an answer that is confidently wrong and present in the option list.
Formats differ in how much they punish this. Aon cut-e spreads the source material across tabbed documents, so a missing second source costs you a tab switch you may not have budgeted for, and the test is negatively marked. Talent Q Elements puts a per-question clock on each item, so a missed source is not a slow item, it is an item you run out of time on. SHL Verify gives you one long clock across eighteen questions, which is more forgiving of one slow item and much less forgiving of a habit of them.
Units, scale and base years
Scale errors are the most common way to arrive at a wrong answer that is also one of the five options. They come in four shapes.
Thousands against millions
An exhibit headed "$m" sitting next to one headed "$000s" is a standard construction, not an accident. If the question combines them, one of the options is your answer multiplied or divided by a thousand. There is no way to catch this after the fact, because the number looks perfectly reasonable. The only defence is reading the header before you start.
Indexed series
A row labelled "index, 2020 = 100" contains no amounts at all. A value of 118 is not 118 of anything, it is 18 per cent above the base year. Two indexed series with different base years cannot be compared directly, and a question that asks which grew faster is answerable from the index while a question that asks which is larger is not. Where the question asks for an absolute figure and the exhibit only gives you an index, the answer is usually that a second exhibit holds the base-year amount.
Percentages of percentages
Europe is 40 per cent of group revenue, and the Netherlands is 25 per cent of European revenue. The Netherlands is therefore 10 per cent of group revenue, not 65 per cent and not 25 per cent. The rule is that nested percentages multiply, and the trap is that the two percentages in the stem have different denominators while looking identical on the page. Whenever you see a percentage, say what it is a percentage of before you use it.
Per-unit and per-period figures
Monthly against annual, per store against total, per head against per household. A table of monthly averages and a question about a year differ by a factor of twelve, and the factor of twelve is in the options. This is the same error as thousands against millions wearing different clothes, and it is caught the same way.
Change against percentage points
This is the most reliably exploited distinction in numerical reasoning, and it is worth being able to state precisely rather than approximately.
Both numbers will be in the option list on any item built around a rate or a margin, and they will not be adjacent, so a glance at the options will not warn you. Two further wrinkles are worth drilling:
- Percentage changes are not symmetric. Going from 80 to 100 is a 25 per cent rise; going from 100 back to 80 is a 20 per cent fall. An item asking about a fall and a recovery is testing exactly this.
- Successive percentage changes do not add. A 10 per cent rise followed by a 10 per cent fall leaves you at 99, not 100. Over three periods the compounded answer and the added answer are far enough apart to be separate options, and the added one is the distractor.
- A percentage of a total can fall while the amount rises.If the total grows faster than the segment, the segment's share drops even though it sold more. Stems that say "share" and stems that say "sales" are different questions.
Ratios, shares and rates
Ratio items look easy and are the second largest source of avoidable losses, because three different objects get written in ways that look alike.
- A ratio is not a fraction of the total. If A to B is 3 to 5, then A is three eighths of the pair, not three fifths. The number of parts is the sum, and the first move on any ratio item is to write down the total number of parts.
- Order matters and the stem controls it."The ratio of staff to managers" and "the ratio of managers to staff" are reciprocals. Where the exhibit presents one and the question asks for the other, the reciprocal is one of the options.
- Ratios across different totals are not comparable as amounts. Two regions can share the same 2 to 1 split while one is four times the size of the other. A question about which region has more of something is not answerable from the ratios alone, and that is frequently the point of the item.
- Scaling a ratio means finding one part first. A 3 to 5 to 8 split of 96,000 has sixteen parts, so one part is 6,000. Working each share as a fraction of the total is slower and generates rounding errors that then fail to match any option exactly, which costs you a second pass.
Korn Ferry Talent Q Elements deserves a specific note here. Its numerical items offer a long option list rather than four or five choices, which is a deliberate design decision: with that many options, an answer you arrived at by a plausible wrong route is still likely to be on the list, and guessing is close to worthless. On that format, checking which denominator the stem wanted is not caution, it is the whole game.
What charts hide that tables do not
A table gives you the number. A chart gives you a picture of the number, and the gap between those is where chart-specific items live.
How the wrong answers were built
Distractors on a professionally written numerical item are not random numbers. Each one is the output of a specific plausible misstep, which is useful to you in two ways: it tells you that an answer matching an option is not evidence you are right, and it lets you work backwards from a surprising option list to the mistake you were about to make.
The formats you will actually meet
The same reading skills are tested through quite different plumbing, and the plumbing changes your tactics more than the content does.
- SHL Verify Numerical. Around eighteen questions on one clock of roughly seventeen to twenty-five minutes, tables and charts, calculator permitted, nothing deducted for a wrong answer. Guess rather than leave anything blank.
- Aon cut-e scales numerical. The odd one out: instead of picking a value, you judge statements as true, false or cannot say against data spread over tabs, with marks deducted for wrong answers. Read the statement first and open only the tab that could settle it.
- Talent Q Elements Numerical. Adaptive, individually timed questions, with a longer clock on the first question attached to a new table because that one includes reading it. Use that first clock to read the exhibit properly; it is being given to you on purpose.
- Kenexa, now hosted by SHL. Twenty five-option questions in twenty minutes, business finance at school level, calculator allowed. One clock across the set, so slow early items take time from later ones.
- Saville Swift Analysis. Eight minutes for the numerical section, which is short enough that reading efficiency dominates and the arithmetic barely matters.
A practice routine that targets reading rather than sums
Once the reading is reliable, the arithmetic is the small half, and the six shortcuts worth learning will make it smaller still. If you are not yet certain which vendor sent your invitation, work that out first, because the marking rule and the delivery format decide how you should be playing the clock. Timed practice in each of these formats is under numerical reasoning.