Statistics, STD2 2026 HSC 19

The number of cars parked in a carpark is recorded each day for thirteen days. The dataset is listed in ascending order:

$12,15,15,17,19,20,22,24,25,27,28,30\ \text{and}\ m.$

What is the interquartile range of this dataset? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---
What is the greatest value of $m$ such that this dataset has no outlier? (2 marks)
--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

a. $11.5$

b. $44$

Show Worked Solution

a. $\text{Dataset has 13 numbers.}$

$\text{Median = 8th value = 22}$

$Q_1=\dfrac{15+17}{2}=16,\quad Q_3=\dfrac{27+28}{2}=27.5$

$IQR=27.5-16 = 11.5$

b. $\text{Find the upper fence:}$

$\text{Upper fence} = Q_3+1.5\times IQR=27.5+1.5(11.5)=44.75$

$\text{Since $m$ is a whole number and must be below 44.75.}$

$m_\text{max}=44$