Civil Service Numerical Reasoning Test Data Interpretation: Tables Syllabus

Why can you not just average two percentages from a table to get the combined percentage?

Because each percentage may be based on a different total (base). You must recombine the actual parts and totals: $\frac{\text{sum of parts}}{\text{sum of totals}} \times 100\%$.

What is the formula for a ratio between two table values $a$ and $b$, and how is it simplified?

The ratio is $a : b$. Simplify by dividing both sides by their greatest common divisor. For example $120 : 80 = 3 : 2$.

What is a 'rate' derived from a table, and give a general formula?

A rate expresses one quantity per unit of another: $\text{rate} = \frac{\text{quantity}}{\text{base quantity}}$, e.g. cases per 1000 people, output per worker, or cost per unit.

A table shows 240 events occurring among 60,000 people. Express this as a rate per 1,000 people.

$\frac{240}{60{,}000} \times 1{,}000 = 4$ per $1{,}000$ people.

How do you express the ratio of one category to the total of a table?

Write category value to total, then simplify: e.g. $50$ out of $200$ is $50 : 200 = 1 : 4$, equivalent to a share of $25\%$.

When combining data from two tables, what is the essential first check before pairing values?

Confirm the tables use matching categories, time periods, and units (scaling). Values can only be combined when they refer to the same defined dimension and scale.

A figure appears in Table 1 (in thousands) and Table 2 (in absolute units). How do you add them correctly?

Convert Table 1's figure to absolute units by multiplying by 1000, then add. Never add the raw tabulated numbers directly.

What is a sensible general process for a multi-step linked calculation across tables?

1) Identify the final quantity required. 2) Find each input value in the correct table. 3) Apply units/scaling. 4) Perform intermediate steps in order, keeping full precision. 5) Round only at the final answer.

Why should you avoid rounding intermediate results in a multi-step table calculation?

Rounding early accumulates error across steps, so the final answer can drift outside the acceptable range. Keep full precision and round only once, at the end.

In a question with a large table, what does 'identifying the relevant data only' mean?

Selecting just the specific rows, columns, and cells the question asks about, and deliberately ignoring distractor figures that are not needed for the calculation.

What is a reliable tactic to avoid using the wrong figure from a dense table?

Read the question first to note the exact category, period and unit required, then locate only those cells — matching every label precisely before reading the value.

What is the formula for absolute change between two periods in a table?

$$\text{Absolute change} = \text{value}_{\text{later}} - \text{value}_{\text{earlier}}$$

What is the formula for percentage change (e.g. year-on-year) from table values?

$$\text{\% change} = \frac{\text{new value} - \text{old value}}{\text{old value}} \times 100\%$$

A figure rose from 250 in 2023 to 300 in 2024. What is the year-on-year percentage change?

$\frac{300 - 250}{250} \times 100\% = \frac{50}{250} \times 100\% = 20\%$ increase.

A value fell from 80 to 68. What is the percentage decrease?

$\frac{68 - 80}{80} \times 100\% = \frac{-12}{80} \times 100\% = -15\%$, i.e. a $15\%$ decrease.

What does 'period-on-period change' mean for table data?

The change in a value from one time period to the next consecutive period (month-on-month, quarter-on-quarter, year-on-year), found by subtracting the earlier period's value from the later one.

How do you rank or order a set of table values from largest to smallest?

Compare the values directly (after ensuring identical units), then arrange them in descending order. The first item is the maximum, the last is the minimum.

When ranking values expressed in different units or scales, what must you do first?

Convert all values to a common unit/scale before comparing, otherwise the ordering can be wrong (e.g. 5 'in millions' beats 800 'in thousands').

How do you identify which category had the largest change between two periods in a table?

Compute the change for each category (absolute or percentage as required), then compare the magnitudes and pick the largest. Specify whether you want the largest increase, decrease, or absolute change.

What is the distinction between the largest absolute change and the largest percentage change?

Absolute change is the raw difference $|a - b|$; percentage change scales that difference by the starting value $\frac{|a-b|}{b}\times100\%$. A small value can show a large percentage change while having a small absolute change, and vice versa.

In data interpretation, what is an anomaly (or outlier) in a table?

A value that deviates markedly from the pattern of the other data — unusually high, low, or inconsistent with the trend — which may signal an error or a notable event worth flagging.

What is a quick way to spot an anomaly across a table row or column?

Scan for a value that breaks the trend or sits far from the others (e.g. a sudden spike or drop), or that makes a total fail to reconcile with its components.

How can a column total be used to check the relevant cell values you read?

Add the individual cells in the column; if they do not match the stated column total, you have mis-read a value, missed an entry, or there is an anomaly to investigate.

What is the formula to increase a base value $V$ by a percentage $p$ from a table?

$$\text{New value} = V \times \left(1 + \frac{p}{100}\right)$$

What is the formula to decrease a base value $V$ by a percentage $p$?

$$\text{New value} = V \times \left(1 - \frac{p}{100}\right)$$

To find the original value before a percentage change, why can't you just reverse the percentage of the new value?

Because the percentage was applied to the original base, not the new value. You must divide: $\text{original} = \frac{\text{new}}{1 \pm \frac{p}{100}}$, not subtract the percentage from the new figure.

A value increased by 25% to reach 500. What was the original value?

$\text{original} = \frac{500}{1.25} = 400$.

How do you find one category's share of a subtotal rather than of the grand total?

Divide the category value by the relevant subtotal (not the grand total): $\frac{\text{category}}{\text{subtotal}} \times 100\%$. Always match the part to the correct base.

In a two-table linked problem, you need 'cost per person'. Table A gives total cost, Table B gives population. What is the process?

Take total cost from Table A and population from Table B (same region/period, matched units), then compute $\frac{\text{total cost}}{\text{population}}$. Confirm both figures share scaling before dividing.

What general checklist helps verify a final data-interpretation answer from a table?

Check: correct cells selected; units/scaling applied; right operation used (change vs share vs average); sensible magnitude; rounding done only at the end; and the answer matches the units the question asks for.