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NSW Y8 Maths

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NSW Y8 Maths Investigating Data Mean and Mode

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Mean and Mode Theory

\begin{multicols}{2} The symbol for the mean is \(\bar{x}\). $$ \bar{x}=\frac{\text { sum of the scores }}{\text { number of scores }} $$ \textbf{Example 1}\\ The mean of the numbers: $$12,12, x, 15,15,16,16,17,19$$ is 15. what is the value of \(x\)?\\ \textbf{Example 1 solution}\\ \(\dfrac{12+12+x+15+15+16+16+17+19}{9}=\dfrac{122+x}{9}\)\\ \(\begin{aligned} \therefore \frac{122+x}{9}&=15 \\ 122+x&=9 \times 15 \\ 122+x&=135 \\ \therefore x&=13 \end{aligned}\) \columnbreak The mode is the score (or scores) that occur the most often.\\ That is the score (or scores) with the highest frequency.\\ \textbf{Example 2}\\ The mode of the numbers: $$12,12, x, 15,15,16,16,17,19$$ is 16. What is the value of \(x\).\\ \textbf{Example 2 solution}\\ For 16 to occur the most frequently then \(x\) must be 16.\\ \hfill \linebreak \hfill \linebreak \hfill \linebreak \hfill \linebreak \end{multicols}

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