CAIE A-Level · Mathematics 9709 · Representation of Data

Measures of Central Tendency and Variation (PS1 – 5.1)

9 min readSyllabus 5.1PreviewBy Uzair Khan

Syllabus objective

Understand and use different measures of central tendency (mean, median, mode) and variation (range, interquartile range, standard deviation), e.g. in comparing and contrasting sets of data; and calculate and use the mean and standard deviation of a set of data (including grouped data) either from the data itself or from given totals Σx and Σx², or coded totals Σ(x − a) and Σ(x − a)², and use such totals in solving problems which may involve up to two data sets.

Introduction

Measures of central tendency (mean, median, mode) locate the "centre" of a data set, while measures of variation (range, interquartile range, standard deviation) describe how spread out the data is. In 9709 PS1, you are expected not only to calculate these measures from raw or grouped data, but also to work efficiently from coded or pre-summarised totals, and to use them to compare two data sets. Questions on this subtopic appear in almost every PS1 paper — often carrying 6–10 marks — and comparing two distributions is a common final part.


Core Concept

Measures of Central Tendency

MeasureDescriptionBest used when
Mean xˉ\bar{x}Arithmetic average; uses all data valuesData is roughly symmetric; no extreme outliers
MedianMiddle value when ordered; splits distribution 50/50Data is skewed or has outliers
ModeMost frequently occurring value (or modal class)Identifying the most common category

Measures of Variation

MeasureDescriptionAdvantage
RangeLargest − SmallestSimple; but very sensitive to outliers
Interquartile range (IQR)Q3Q1Q_3 - Q_1Robust to outliers
Standard deviation σ\sigmaRoot-mean-square deviation from the meanUses every data point; most powerful measure

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