| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2020 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Interpret or analyse given back-to-back stem-and-leaf |
| Difficulty | Easy -1.2 This is a straightforward stem-and-leaf interpretation question requiring basic statistical skills: reading values from a diagram, finding median and quartiles by counting positions (n=19, so 10th value for median), calculating IQR, drawing box plots, and making simple comparative statements. All techniques are routine recall with no problem-solving or novel insight required, making it easier than average A-level questions. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| \(A\) | \(B\) | |||||||||||
| 21 | 1 | 2 | 4 | |||||||||
| 7 | 6 | 3 | 0 | 22 | 2 | 4 | 5 | 5 | 6 | |||
| 8 | 7 | 4 | 3 | 1 | 1 | 23 | 0 | 2 | 6 | 8 | 9 | |
| 5 | 5 | 5 | 3 | 2 | 24 | 3 | 3 | 4 | 6 | |||
| 4 | 3 | 1 | 0 | 25 | 6 | |||||||
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Median \(= 0.238\) | B1 | |
| \(UQ = 0.245\), \(LQ = 0.231\), so \(IQR = 0.245 - 0.231\) | M1 | |
| \(0.014\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Machine A: min \(0.220\), \(LQ = 0.231\) FT, \(M = 0.238\) FT, \(UQ = 0.245\) FT, max \(0.254\); Machine B: min \(0.211\), \(LQ = 0.224\), \(M = 0.232\), \(UQ = 0.243\), max \(0.256\) | ||
| Medians and quartiles correctly plotted for \(A\) or \(B\) | B1 | |
| End points correct for \(A\) or \(B\) | B1 | |
| Completely correct, including scale | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| Lengths of rods produced by machine \(A\) are longer | B1 | Comparison of central tendency |
| Lengths of rods produced by machine \(A\) are less spread out | B1 | Comparison of spread |
## Question 3(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| Median $= 0.238$ | B1 | |
| $UQ = 0.245$, $LQ = 0.231$, so $IQR = 0.245 - 0.231$ | M1 | |
| $0.014$ | A1 | |
---
## Question 3(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| Machine A: min $0.220$, $LQ = 0.231$ FT, $M = 0.238$ FT, $UQ = 0.245$ FT, max $0.254$; Machine B: min $0.211$, $LQ = 0.224$, $M = 0.232$, $UQ = 0.243$, max $0.256$ | | |
| Medians and quartiles correctly plotted for $A$ or $B$ | B1 | |
| End points correct for $A$ or $B$ | B1 | |
| Completely correct, including scale | B1 | |
---
## Question 3(c):
| Answer | Mark | Guidance |
|--------|------|----------|
| Lengths of rods produced by machine $A$ are longer | B1 | Comparison of central tendency |
| Lengths of rods produced by machine $A$ are less spread out | B1 | Comparison of spread |
---3 Two machines, $A$ and $B$, produce metal rods of a certain type. The lengths, in metres, of 19 rods produced by machine $A$ and 19 rods produced by machine $B$ are shown in the following back-to-back stem-and-leaf diagram.
\begin{table}[h]
\begin{center}
\begin{tabular}{ l l l l l l | l | l l l l l }
\multicolumn{6}{c|}{$A$} & \multicolumn{7}{c}{$B$} \\
\hline
& & & & & & 21 & 1 & 2 & 4 & & & \\
& & 7 & 6 & 3 & 0 & 22 & 2 & 4 & 5 & 5 & 6 & \\
& & & & & & & & & & & & \\
8 & 7 & 4 & 3 & 1 & 1 & 23 & 0 & 2 & 6 & 8 & 9 & \\
& 5 & 5 & 5 & 3 & 2 & 24 & 3 & 3 & 4 & 6 & & \\
& & 4 & 3 & 1 & 0 & 25 & 6 & & & & & \\
\end{tabular}
\captionsetup{labelformat=empty}
\caption{Key: 7 | 22 | 4 means 0.227 m for machine $A$ and 0.224 m for machine $B$.}
\end{center}
\end{table}
\begin{enumerate}[label=(\alph*)]
\item Find the median and the interquartile range for machine $A$.\\
It is given that for machine $B$ the median is 0.232 m , the lower quartile is 0.224 m and the upper quartile is 0.243 m .
\item Draw box-and-whisker plots for $A$ and $B$.\\
\includegraphics[max width=\textwidth, alt={}, center]{a3b3ebd1-db9e-4552-9abe-bfdeba786d02-05_812_1205_616_511}
\item Hence make two comparisons between the lengths of the rods produced by machine $A$ and those produced by machine $B$.
\end{enumerate}
\hfill \mbox{\textit{CAIE S1 2020 Q3 [8]}}