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Analysing Frequency Tables Theory
![\begin{multicols}{2} \textbf{Example 1}\\ From the data given in the frequency table find:\\ \textbf{i)} The range\\ \textbf{ii)} The mode\\ \textbf{iii)} The median\\ \textbf{iv)} The mean\\ \begin{center} \begin{tabular}{|c|c|} \hline Score & Frequency \\ \hline 4 & 1 \\ \hline 5 & 2 \\ \hline 6 & 3 \\ \hline 7 & 4 \\ \hline 8 & 3 \\ \hline 9 & 2 \\ \hline 10 & 1 \\ \hline \end{tabular} \end{center} \hfill \linebreak \textbf{Example 1 solution}\\ \textbf{i)} \(\begin{aligned}[t] \text { Range } & =\text { highest score }- \text { lowest score } \\ & =10-4 =6 \end{aligned}\)\\ \textbf{ii)} The mode \(=\) score, with highest frequency\\ \(\therefore \text { mode }=7\)\\ \textbf{iii)} Median \(=\) average of the two middle scores of an even number of scores\\ Total number of scores \(=16\)\\[3pt] \(\begin{aligned} \text { Median } & =\frac{8 \text {th }+ 9\text {th score }}{2} \\ & =\frac{7+7}{2}=7 \end{aligned}\)\\[3pt] \textbf{iv)} \(\begin{aligned}[t] \text { Mean } & =\frac{\text { total of scores }}{\text { number of scores }} \\ & =\frac{4+10+18+28+24+18+10}{16}\\ &=7 \end{aligned}\) \columnbreak \textbf{Example 2}\\ From the scores on a test: \begin{center} \(5,5,6,6,6,6,7,7,7,8,8,8,8,8,9,9\) \end{center} set up a frequency table and determine the mean of these scores.\\ \textbf{Example 2 solution}\\ \begin{center} \begin{tabular}{|c|c|c|} \hline Score (x) & Frequency (f) & \(\mathrm{fx}\) \\ \hline 5 & 2 & 10 \\ \hline 6 & 4 & 24 \\ \hline 7 & 3 & 21 \\ \hline 8 & 5 & 40 \\ \hline 9 & 2 & 18 \\ \hline & 16 & 113 \\ \hline \end{tabular} \end{center} \hfill \linebreak \(\begin{aligned} \bar{x}&=\frac{113}{16} \\ \bar{x}&=7.1 \end{aligned}\) \end{multicols}](/media/ja3aapbx/9224.png)
NSW Y8 Maths Investigating Data Analysing Frequency Tables
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