Resources for Frequency Histogram and Polygons
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Questions
2
With Worked SolutionClick Here -
Video Tutorials
2
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Frequency Histogram and Polygons Theory
![\begin{multicols}{2} \textbf{Example 1}\\ The histogram shows the number of students and their scores out of ten.\\ \begin{center} \resizebox{0.5\textwidth}{!}{ \begin{tikzpicture} \draw[step=0.5cm, line width=0.5pt, black!30!white] (-0.5,0) grid (10,5); \draw[line width=1pt] (-0.5,0)--node[below,yshift=-0.7cm] {\Large \bf Test Score} (10.5,0); \draw[line width=1pt] (-0.5,0) edge (-0.5,5); \foreach \bar/\height in {3/1,4/2,5/3,6/4,7/2,8/1,9/2} \draw[fill=blue!50] (\bar-0.5,0) rectangle (\bar+0.5,\height); \foreach \y in {1,2,3,4,5} \draw[line width=1pt] (-0.5, \y ) edge (-0.3, \y) node[black,anchor=north,xshift=-0.5cm,yshift=0.3cm]{\Large\(\y\)}; \foreach \x in {0,1,2,3,4,5,6,7,8,9,10} \draw[line width=1pt] (\x, 0)--(\x, 0.2) node[black,anchor=north,yshift=-0.2cm]{\Large\(\x\)}; \node[xshift=1cm,align=center] at (-3.5,2.5) {\Large \bf Number\\ \Large \bf of\\ \Large \bf students}; \end{tikzpicture} } \end{center} \textbf{i)} How many students did the test?\\ \textbf{ii)} Find the mode.\\ \textbf{iii)} Find the range\\ \textbf{iv)} Find the median\\ \textbf{v)} Find the mean.\\ \textbf{Example 1 solution}\\ \textbf{i)} \(\begin{aligned}[t] \text { Number of students } & =1+2+3+4+2+1+2 \\ & =15 \end{aligned}\)\\ \textbf{ii)} The score with the highest frequency \(=6\)\\ \(\begin{aligned}\quad \therefore \text { Mode }=6 \end{aligned}\)\\ \textbf{iii)} \(\begin{aligned}[t] \text { Range } & =\text { highest score }- \text { lowest score } \\ & =9-3=6 \end{aligned}\)\\ \textbf{iv)} The median is the middle score: \(15 \div 2=7.5\)\\ \(\begin{aligned}\quad \therefore \end{aligned}\) The median is the 8th score\\ \(\begin{aligned}\quad\text { Median }=6\end{aligned}\)\\ \textbf{v)} \(\begin{aligned}[t] \text{The mean } &= \frac{\text{sum of all scores}}{\text{number of scores}}\\ \text { mean } & =\frac{3+4+4+\cdots+8+9+9}{15} \\ & =\frac{90}{15}=6 \end{aligned}\) \columnbreak \textbf{Example 2}\\ The frequency polygon has the same data as in example 1, with the polygon drawn over the frequency histogram. \begin{center} \resizebox{0.5\textwidth}{!}{ \begin{tikzpicture} \draw[step=0.5cm, line width=0.5pt, black!30!white] (-0.5,0) grid (10,5); \draw[line width=1pt] (-0.5,0)--node[below,yshift=-0.7cm] {\Large \bf Test Score} (10.5,0); \draw[line width=1pt] (-0.5,0) edge (-0.5,5); \foreach \bar/\height in {3/1,4/2,5/3,6/4,7/2,8/1,9/2} \draw[fill=blue!50] (\bar-0.5,0) rectangle (\bar+0.5,\height); \foreach \y in {1,2,3,4,5} \draw[line width=1pt] (-0.5, \y ) edge (-0.3, \y) node[black,anchor=north,xshift=-0.5cm,yshift=0.3cm]{\Large\(\y\)}; \foreach \x in {0,1,2,3,4,5,6,7,8,9,10} \draw[line width=1pt] (\x, 0)--(\x, 0.2) node[black,anchor=north,yshift=-0.2cm]{\Large\(\x\)}; \node[xshift=1cm,align=center] at (-3.5,2.5) {\Large \bf Number\\ \Large \bf of\\ \Large \bf students}; \draw[line width=1.5pt] (2,0)--(3,1)--(4,2)--(5,3)--(6,4)--(7,2)--(8,1)--(9,2)--(10,0); \end{tikzpicture} } \end{center} \textbf{i)} What percentage of students scored greater than 6?\\ \textbf{ii)} What percentage of students scored less than 6?\\ \textbf{Example 2 solution}\\ \textbf{i)} Total number of students \(=15\)\\ \(\text { Number of students above } \begin{aligned}[t] 6 & =2+1+2 \\ & =5 \end{aligned}\)\\ \(\begin{aligned} \therefore \% \text { above } 6 & =\frac{5}{15} \times 100 \% \\ & =33 \frac{1}{3} \% \end{aligned}\)\\[3pt] \textbf{ii)} \(\text { Number of students below } \begin{aligned}[t] 6 & =1+2+3 \\ & =6 \end{aligned}\)\\ \(\begin{aligned} \therefore \% \text { below } 6 & =\frac{6}{15} \times 100 \% \\ & =40 \% \end{aligned}\) \end{multicols}](/media/4c0ktagi/9226.png)