| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | November |
| Marks | 6 |
| 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 | Moderate -0.8 This is a straightforward question requiring reading values from a stem-and-leaf diagram to find median and quartiles, then drawing box plots. The stem-and-leaf is clearly presented with a key, and part (ii) provides all values for group B. This involves standard recall of definitions and routine calculations with no problem-solving insight required, making it easier than average. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| \(A\) | \(B\) | |||
| (4) | 4200 | 20 | 567 | (3) |
| (5) | 98500 | 21 | 122377 | (6) |
| (8) | 98753222 | 22 | 1356689 | (7) |
| (6) | 876521 | 23 | 45788999 | (8) |
| (3) | 863 | 24 | 2456788 | (7) |
| (1) | 0 | 25 | 0278 | (4) |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| median \(= 0.225\); \(LQ = 0.215\): \(UQ = 0.236\) | B1 | Correct median (\(Q_2\)) |
| \(IQR = 0.236 - 0.215\) | M1 | \(0.232 < UQ\ (Q_3) < 0.238 - 0.204 < LQ\ (Q_1) < 0.219\) |
| \(= 0.021\) | A1 | www; Omission of all decimal points MR-1; If M0 awarded SCB1 for both \(LQ = 0.215\): \(UQ = 0.236\) seen |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Box plot diagram with linear scale 0.20 to 0.26 | B1 | Linear scale between 0.20 to 0.26 (condone omission of 0.26) axis labelled (time and seconds), at least one box plot attempted, no lines through boxes, whiskers not at corner of boxes |
| Labelled correct graph for A: \(0.200,\ 0.215,\ 0.225,\ 0.236,\ 0.250\) | B1 ft | Labelled correct graph for A (ft their median/quartiles), condone lines through boxes, whiskers at corner of boxes |
| Labelled correct graph for B: \(0.205,\ 0.217,\ 0.235,\ 0.245,\ 0.258\) | B1 | Labelled correct graph for B, condone lines through boxes, whiskers at corner of boxes. SC If B0B0 scored because graphs not labelled/labels reversed SCB1 if both 'correct'. Penalty MR-1 if graphs plotted on separate axes unless both scales align exactly. |
## Question 2(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| median $= 0.225$; $LQ = 0.215$: $UQ = 0.236$ | **B1** | Correct median ($Q_2$) |
| $IQR = 0.236 - 0.215$ | **M1** | $0.232 < UQ\ (Q_3) < 0.238 - 0.204 < LQ\ (Q_1) < 0.219$ |
| $= 0.021$ | **A1** | www; Omission of all decimal points **MR-1**; If M0 awarded **SCB1** for both $LQ = 0.215$: $UQ = 0.236$ seen |
## Question 2(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Box plot diagram with linear scale 0.20 to 0.26 | **B1** | Linear scale between 0.20 to 0.26 (condone omission of 0.26) axis labelled (time and seconds), at least one box plot attempted, no lines through boxes, whiskers not at corner of boxes |
| Labelled correct graph for A: $0.200,\ 0.215,\ 0.225,\ 0.236,\ 0.250$ | **B1 ft** | Labelled correct graph for A (ft their median/quartiles), condone lines through boxes, whiskers at corner of boxes |
| Labelled correct graph for B: $0.205,\ 0.217,\ 0.235,\ 0.245,\ 0.258$ | **B1** | Labelled correct graph for B, condone lines through boxes, whiskers at corner of boxes. **SC** If B0B0 scored because graphs not labelled/labels reversed SCB1 if both 'correct'. Penalty **MR-1** if graphs plotted on separate axes unless both scales align exactly. |2 The following back-to-back stem-and-leaf diagram shows the reaction times in seconds in an experiment involving two groups of people, $A$ and $B$.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multicolumn{2}{|c|}{$A$} & \multicolumn{3}{|c|}{$B$} \\
\hline
(4) & 4200 & 20 & 567 & (3) \\
\hline
(5) & 98500 & 21 & 122377 & (6) \\
\hline
(8) & 98753222 & 22 & 1356689 & (7) \\
\hline
(6) & 876521 & 23 & 45788999 & (8) \\
\hline
(3) & 863 & 24 & 2456788 & (7) \\
\hline
(1) & 0 & 25 & 0278 & (4) \\
\hline
\end{tabular}
\end{center}
Key: 5 | 22 | 6 means a reaction time of 0.225 seconds for $A$ and 0.226 seconds for $B$\\
(i) Find the median and the interquartile range for group $A$.\\
The median value for group $B$ is 0.235 seconds, the lower quartile is 0.217 seconds and the upper quartile is 0.245 seconds.\\
(ii) Draw box-and-whisker plots for groups $A$ and $B$ on the grid.\\
\includegraphics[max width=\textwidth, alt={}, center]{62812433-baee-490a-bad4-b6b0f917c234-03_805_1495_1729_365}
\hfill \mbox{\textit{CAIE S1 2018 Q2 [6]}}