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 \(\text{By inspection of box plot,}\ \ IQR=\dfrac{2}{3}\times \text{range}\) \(\text{ln options A, B and C (given 16 data points):}\) \(Q_1\ \text{(4th data point)}\ \rightarrow \text{2nd column}\) \(Q_3\ \text{(13th data point)}\ \rightarrow \text{6th column}\) \(\text{Since}\ IQR=\dfrac{2}{3}\times \text{range}\ \Rightarrow\ \text{histograms are possible.}\) \(\text{ln option D:}\) \(Q_1 \rightarrow \text{3rd column}\) \(Q_3 \rightarrow \text{5th column}\) \(\text{Since}\ IQR=\dfrac{1}{3} \times \text{range}\ \Rightarrow\ \text{not possible.}\) \(\Rightarrow D\)