Statistical Officer / Government Statistical Service (GSS) Assessment Numerical Reasoning and Quantitative Aptitude Syllabus

In a grouped/stacked bar chart, how do you find the value of a single segment?

Read the cumulative value at the top of the segment and subtract the cumulative value at the bottom of that segment. The segment's value is the difference between its upper and lower boundaries, not the top reading alone.

What is a robust general process for any multi-step calculation from data?

1) Identify exactly what is asked. 2) Locate the relevant figures and note their units. 3) Plan the operations in order. 4) Carry out the calculation step by step. 5) Check the answer for plausibility and correct units.

Why should you keep full precision until the final step of a multi-step calculation?

Rounding intermediate results introduces rounding error that can compound, giving a wrong final answer. Keep extra decimal places (or use the calculator memory) throughout and round only the final value.

How do you calculate a percentage of a percentage? Example: $30\%$ of a group, of which $40\%$ meet a condition.

Multiply the two as decimals: $0.30 \times 0.40 = 0.12 = 12\%$ of the whole. For absolute numbers, apply each percentage in turn to the running total.

How do you combine two groups to find an overall (weighted) percentage?

Add the actual counts, not the percentages. Overall $\% = \frac{\text{total favourable}}{\text{total whole}} \times 100$. Averaging two percentages directly is only valid if the group sizes are equal.

How do you express the difference between two periods as a percentage increase or decrease?

Use $\frac{\text{later} - \text{earlier}}{\text{earlier}} \times 100\%$. Always divide by the earlier (baseline) value. Dividing by the wrong base is a common trap when comparing trends.

What is the difference between an absolute change and a relative (percentage) change in trend analysis?

Absolute change is the raw difference (e.g. $+200$ units). Relative change expresses that difference as a proportion of the starting value (e.g. $+10\%$). A large absolute change can be a small relative change and vice versa.

When comparing trends across categories of very different sizes, why are percentages often more useful than raw figures?

Percentages normalise for size, allowing fair comparison of growth rates. A small category can grow by a large percentage with a tiny absolute change, while a large category's small percentage change is a big absolute change.

What is compound growth, and what is its formula over $n$ periods?

Compound growth applies each period's growth to the new total. $$A = P\left(1 + \frac{r}{100}\right)^{n}$$ where $P$ is the initial amount, $r$ the percentage rate per period, and $n$ the number of periods.

How do you calculate simple interest?

$$I = \frac{P \times r \times t}{100}$$ where $P$ is the principal, $r$ the annual rate (as a percentage), and $t$ the time in years. The total amount is $P + I$.

How do you compute VAT and the gross price from a net price at the standard UK rate of $20\%$?

VAT $= \text{net} \times 0.20$; gross $= \text{net} \times 1.20$. To find the net from a gross price, divide by $1.20$ (the VAT portion of a gross price is $\frac{\text{gross}}{6}$).

How do you calculate the remaining balance of a budget after several expenditures?

Sum all expenditures, then subtract from the total budget: $\text{remaining} = \text{budget} - \sum \text{spend}$. To express as a proportion used, divide total spend by the budget.

How do you find what percentage of a budget a particular line item represents?

Divide the item's cost by the total budget and multiply by $100$: $\frac{\text{item}}{\text{total budget}} \times 100\%$. This is the share of spend for that item.

What is the formula for the arithmetic mean of a data set?

$$\bar{x} = \frac{\sum x}{n}$$ the sum of all values divided by the number of values $n$.

What is the median, and how do you find it for an even number of values?

The median is the middle value of an ordered data set. For an even count, it is the mean of the two central values. Always sort the data first.

What is the mode, and when is it the most useful average?

The mode is the most frequently occurring value. It is most useful for categorical data or for finding the most common outcome, and a data set may have no mode or several modes.

What is the range, and what does it tell you about a data set?

$$\text{range} = \text{maximum} - \text{minimum}$$ It measures the spread (dispersion) of the data. It is simple but sensitive to outliers.

How do you compute the mean from a frequency table?

Multiply each value by its frequency, sum these products, then divide by the total frequency: $$\bar{x} = \frac{\sum f x}{\sum f}$$

Why can the mean be misleading, and what is a more robust alternative?

The mean is sensitive to outliers and skewed distributions, which can pull it away from the typical value. The median is more robust because it is unaffected by extreme values.

What do the quartiles and the interquartile range (IQR) measure?

Quartiles divide ordered data into four equal parts: $Q_1$ (lower), $Q_2$ (median), $Q_3$ (upper). The IQR $= Q_3 - Q_1$ measures the spread of the middle $50\%$ of the data and is resistant to outliers.

How do you find the next term of an arithmetic sequence, and what is its general term?

Add the common difference $d$ each time. The $n$th term is $$a_n = a_1 + (n-1)d$$ where $a_1$ is the first term.

How do you identify a geometric sequence, and what is its general term?

Each term is found by multiplying the previous term by a constant ratio $r$. The $n$th term is $$a_n = a_1 r^{\,n-1}$$

How do you find the common difference or ratio when a sequence's type is not obvious?

Check successive differences (later minus earlier): if constant, it is arithmetic. If the differences are not constant, check the ratios of successive terms: if constant, it is geometric. Otherwise look for squares, primes, or alternating patterns.

Identify the pattern and next term: $2, 6, 12, 20, 30, \ldots$

The differences increase by $2$ each time ($4, 6, 8, 10, \ldots$), so the next difference is $12$ and the next term is $42$. The terms follow $a_n = n(n+1)$.

What is an effective time-management strategy for a timed quantitative test with $N$ questions?

Divide total time by the number of questions to get an average pace (e.g. $30$ minutes for $20$ questions = $90$ seconds each). Track checkpoints, and if a question exceeds its budget, flag it and move on to avoid losing easy marks later.

When stuck on a difficult quantitative question under time pressure, what is the recommended approach?

Skip it, secure the answerable questions first, and return if time allows. If you must answer (no negative marking), eliminate implausible options and make an educated estimate rather than leaving it blank.

How can estimation and rounding speed up calculations and catch errors?

Round figures to convenient values to get an approximate answer quickly (e.g. $\pounds 1{,}980 \approx \pounds 2{,}000$). Use this estimate to sense-check the exact calculation and to eliminate answer options that are far off.

What practical tips improve accuracy when using an on-screen calculator?

Type carefully and watch operator precedence (use brackets), use the memory functions ($M+$, $MR$) to store intermediate results, re-enter and re-check a calculation if the result looks implausible, and confirm whether percentages are entered as decimals or with a $\%$ key.

What are common 'traps' to watch for in reading-data and word problems?

Mismatched units or scale factors (thousands vs millions), confusing percentage points with percent, dividing by the wrong base, answering a different quantity than asked, and ignoring footnotes or 'except' / 'excluding' wording. Always re-read what is being asked.

Why must you confirm the units of your final answer before submitting?

An otherwise correct calculation gives the wrong answer if the units are off, for example giving a result in pounds when thousands of pounds were required, or minutes when hours were asked. Match the answer's units and rounding to exactly what the question requested.