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NSW Y12 Maths - Advanced Descriptive Statistics Measures of Central Tendency

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Measures of Central Tendency Theory

There are three measunes of central tendency: the mean, the median and the mode. \\ \textbf{Example 1}\\ Given the data: \(3,4,5,5,6,8\) calculate\\ (i) the mean\\ (ii) the median\\ (ii) the mode\\ \textbf{Example 1 solution}\\ $\begin{aligned} \text{i) } \quad \text { mean } \bar{x} & =\frac{3+4+5+5+6+8}{6} \\ & =\frac{31}{6} \\ & =5.17\end{aligned}$\\ (ii) The median is the middle score There are two middle scores 5 and 5 $\begin{aligned} \therefore \text { median } & =\frac{5+5}{2} \\ & =5 \end{aligned}$\\ (iii) The mode is the score which occurs most frequently.\\ There are 2 5's\\ \(\therefore\) Mode \(=5\).\\

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