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Statistics, STD2 S1 2024 HSC 15 MC

Some data are used to create a box plot shown.
 

A histogram is created from the same set of data.

Which of these histograms is NOT possible for the given box plot?
 


 

Show Answers Only

\(D\)

Show Worked Solution

\(\text{By inspection of box plot,}\ \ IQR=\dfrac{2}{3}\times \text{range}\)

\(\text{ln options A, B and C (given 16 data points):}\)

\(Q_1\ \text{(4th data point)}\ \rightarrow \text{2nd column}\)

\(Q_3\ \text{(13th data point)}\  \rightarrow \text{6th column}\)

\(\text{Since}\ IQR=\dfrac{2}{3}\times \text{range}\ \Rightarrow\ \text{histograms are possible.}\)
 

\(\text{ln option D:}\)

\(Q_1  \rightarrow \text{3rd column}\)

\(Q_3 \rightarrow \text{5th column}\)

\(\text{Since}\ IQR=\dfrac{1}{3} \times \text{range}\ \Rightarrow\ \text{not possible.}\)

\(\Rightarrow D\)

♦♦♦ Mean mark 9%.

Filed Under: Summary Statistics - Box Plots (Std 2), Summary Statistics - Box Plots (Std2-2027) Tagged With: 2adv-std2-common, Band 6, smc-6313-50-Other, smc-825-50-Other

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