EPSO Numerical Reasoning key terms

The unit used to describe the arithmetic difference between two percentages, rather than their relative change. A rise from 20% to 25% is 5 percentage points but a 25% relative increase.

The difference between a new value and an original value, divided by the original value and expressed as a percentage. The original value is always the denominator.

The original or reference quantity against which a change or comparison is measured. Identifying it correctly determines whether a percentage is computed on the right denominator.

A change expressed as a proportion of the starting figure, so that identical absolute movements can represent very different relative movements depending on the size of the base.

The simple arithmetic difference between two values in their own units, without dividing by any base. It shows size of movement but not its significance relative to the starting level.

Recovering an original amount when only the post-change value and the percentage rate are known. It requires dividing by one plus or minus the rate, not subtracting the percentage.

Repeated application of a percentage rate to an amount that already includes earlier increases, so that the growth accelerates. Total growth exceeds the simple sum of the individual rates.

A comparison of two or more quantities showing how many times one contains another. It carries no units and is scaled by multiplying or dividing all parts by the same number.

A statement that two ratios are equal, or a share of a total expressed as a fraction of that total. It allows an unknown quantity to be found from a known corresponding quantity.

A ratio comparing one component with the total of all components, often written as a fraction or percentage. It differs from a part-to-part ratio, which compares components only with each other.

The multiplier that converts a value in one version of a figure into the corresponding value in another, such as from a map or model to reality. Areas scale by its square and volumes by its cube.

A technique that first reduces a relationship to the value of one unit, then multiplies by the number of units required. It converts proportional reasoning into two simple arithmetic steps.

The sum of a set of values divided by how many values there are. It is sensitive to extreme values, which can pull it far from the typical observation.

An average in which each value is multiplied by a weight reflecting its importance or group size, then divided by the total of the weights. It equals the mean of the pooled data.

The overall average of two or more groups, computed from each group's mean and size rather than from individual observations. It always lies between the smallest and largest group means.

The middle value of a data set once the values are ranked in order. With an even count it is the mean of the two central values, and it resists distortion by outliers.

An observation lying far from the rest of the data. It can inflate or deflate a mean sharply while leaving the median almost unchanged.

The distance covered per unit of time, found by dividing distance by time. Units must be consistent, so minutes are usually converted to hours before dividing.

Total distance travelled divided by total time taken for the whole journey. It is not the simple mean of the speeds used on each leg unless the legs took equal time.

The reciprocal of the arithmetic mean of reciprocals, used when averaging rates over equal distances. For two equal-distance legs at speeds a and b it equals 2ab divided by a plus b.

Changing a quantity from one measurement unit to another by multiplying by a conversion factor, such as kilometres per hour to metres per second. Errors here are a common source of wrong answers.

The approximate scale of a number, usually its nearest power of ten. Estimating it lets a candidate eliminate implausible answer options without exact computation.

Rounding figures to convenient values to obtain a quick approximate result. In timed tests it is used to select among widely separated answer options before any precise calculation.

Replacing a number by a nearby value with fewer significant digits. Repeated rounding can accumulate error, so it should be applied late or in a controlled direction.

The digits of a number that carry meaningful information about its precision. Leading zeros never count, and trailing zeros count only when a decimal point is present.

Knowledge that fractions such as one eighth, one sixth or three quarters correspond to fixed decimal values. Recognising these speeds up comparisons and mental division.

The value obtained by dividing one by a number, so that the product of the two equals one. Reciprocals underlie division of fractions and averaging of rates.

The distinction between a raw count or amount and the same figure expressed as a share, rate or index. Charts can mislead when the two are confused or mixed on one scale.

The range and interval marked on a chart axis. A truncated or non-zero starting point exaggerates visual differences between bars or lines.

A circular chart in which each sector's angle is proportional to its share of the total. It shows composition only, and sector sizes cannot be compared across different totals.

A value expressing a quantity relative to a fixed base period, usually set to 100. It allows series with different units to be compared and rebased to a new reference year.

Adjusting money amounts, such as salaries or contract prices, in line with a price index to preserve real value. The adjustment is a percentage change applied to the base amount.

A nominal figure is stated in current money, while a real figure has been deflated by a price index to remove inflation. Real comparisons require both series on the same price basis.

Interest calculated on the principal plus previously accumulated interest. The balance grows by a fixed factor each period rather than by a fixed amount.

Interest calculated only on the original principal for each period, so the amount added stays constant. It grows linearly, unlike compound interest.

The fraction of a task completed per unit of time by one worker, machine or team. Rates add when resources work simultaneously on the same task.

The sum of the individual rates of all contributors working together. The time to finish is one divided by that combined rate.

Distributing a limited quantity of staff, budget or capacity across activities according to a rule or constraint. Solutions must respect the constraint as well as the proportional shares.

An arrangement of items in which order matters. The number of ways to arrange all n distinct items is n factorial, which grows extremely quickly.

A selection of items in which order does not matter, so that rearranging the chosen items counts as the same selection. It equals the permutation count divided by the factorial of the number chosen.

The product of all whole numbers from one up to a given number, written with an exclamation mark. Zero factorial is defined as one.

Events that cannot occur in the same trial, so the probability of either happening is the sum of their separate probabilities. Overlapping events require subtracting the joint probability.

Events whose outcomes do not influence each other, so the probability of both occurring is the product of their individual probabilities. Sampling without replacement breaks independence.

A question type asking whether the supplied statements are enough to determine a unique answer, not what the answer is. Solving the value is unnecessary and wastes time.

A condition whose truth guarantees the conclusion, though other conditions might also guarantee it. In sufficiency questions one statement alone may settle the matter.

A condition that must hold for the conclusion to be true, but which may not be enough on its own. Confusing it with a sufficient condition is a frequent reasoning error.

A single case in which a proposed statement fails, proving the statement false. It is the fastest way to reject a general claim in numerical validation questions.