Question 1
The following data shows the times (minutes) taken by 12 students to complete a puzzle:
\(8,\;12,\;15,\;9,\;21,\;14,\;18,\;11,\;25,\;10,\;16,\;13\)
(a)Find the median, lower quartile (\(Q_1\)), and upper quartile (\(Q_3\)).
(b)Calculate the IQR.
(c)Identify any outliers using the rule: outlier if \(Q_3+1.5 imes ext{IQR}\).
(a)
Sort: 8,9,10,11,12,13,14,15,16,18,21,25
Median \(= frac{13+14}{2}=13.5\); \(Q_1= frac{10+11}{2}=10.5\); \(Q_3= frac{16+18}{2}=17\)
Answer
\(Q_1=10.5,\; ext{Median}=13.5,\;Q_3=17\)
(c)
Bounds
Lower: \(10.5-9.75=0.75\); Upper: \(17+9.75=26.75\)
Answer
No outliers (all values within bounds)
Question 2
The cumulative frequency table below shows the marks of 80 students:
\[egin{array}{c|c} ext{Mark}\leq& ext{Cumulative Freq}\\hline20&5\30&14\40&30\50&54\60&70\70&78\80&80\end{array}\]
(a)Estimate the median and quartiles from a cumulative frequency graph.
(b)Draw a box-and-whisker plot.
(a)
Read off at \(n/2=40,\;n/4=20,\;3n/4=60\)
Median \(pprox50\); \(Q_1pprox38\); \(Q_3pprox58\)
Answer
\(Q_1pprox38,\; ext{Median}pprox50,\;Q_3pprox58\)
(b)
Box plot
Min \(=20\), \(Q_1=38\), Med \(=50\), \(Q_3=58\), Max \(=80\)
Question 3
Two classes sit the same test. Their results are summarised:
\[egin{array}{l|ccccc}& ext{Min}&Q_1& ext{Med}&Q_3& ext{Max}\\hline ext{Class A}&42&55&64&72&90\ ext{Class B}&38&48&60&78&95\end{array}\]
(a)Compare the median scores.
(b)Compare the spread using the IQR.
(c)Which class performed more consistently? Justify.
(a)
Answer
Class A median (64) is higher than Class B (60), suggesting A performed better on average.
(b)
IQRs
Class A: \(72-55=17\); Class B: \(78-48=30\)
Answer
Class B has a larger IQR — more spread out.
(c)
Answer
Class A — smaller IQR indicates more consistent performance.