| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2002 |
| Session | November |
| Marks | 9 |
| 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 data interpretation question requiring basic statistical skills: reading a stem-and-leaf diagram, finding median and quartiles by counting positions, drawing box plots, and making simple comparative observations. All techniques are routine for S1 level with no problem-solving or novel insight required. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Country \(P\) | Country \(Q\) | |
| 5 | 15 | |
| 6 | 2348 | |
| 98764 | 7 | 1345677889 |
| 886653 | 8 | 2367788 |
| 977655542 | 9 | 0224 |
| 54431 | 10 | 45 |
| Answer | Marks | Guidance |
|---|---|---|
| Part (i): \(LQ = 72,\) or \(73\) or \(71.5\) only; \(\text{median} = 78,\) \(UQ = 88\) or \(87.75\) only | B1 | Accept \(Q_1, Q_2, Q_3\) |
| B1 | \(LQ\) \(UQ\) muddle scores B1 B0 and possibly B1 for median | |
| B1 | 3 | |
| Part (ii): | B1 | For only one numbered linear scale |
| B1 | For country \(P\) all correct on linear scale | |
| B1 ft | For \(Q\) all correct on linear scale | |
| B1 | 4 | For P and Q labelled, weights or kg shown |
| SR non linear scale max B0 B1 B0 B1 or max B0 B1 B0 B1 if one error in an otherwise linear scale | ||
| NB No outliers | ||
| Part (iii): people heavier in \(P\) than in \(Q\); weights more spread out in \(Q\) | B1 | Or equivalent statement |
| B1 | 2 | Or equivalent statement |
| Cannot have two statements saying the equivalent of the same category (wts, spread, skewness). Must have the same statement relating to P and to Q. |
**Part (i):** $LQ = 72,$ or $73$ or $71.5$ only; $\text{median} = 78,$ $UQ = 88$ or $87.75$ only | B1 | Accept $Q_1, Q_2, Q_3$
| B1 | $LQ$ $UQ$ muddle scores B1 B0 and possibly B1 for median
| B1 | 3
**Part (ii):** | B1 | For only one numbered linear scale
| B1 | For country $P$ all correct on linear scale
| B1 ft | For $Q$ all correct on linear scale
| B1 | 4 | For P and Q labelled, weights or kg shown
| | SR non linear scale max B0 B1 B0 B1 or max B0 B1 B0 B1 if one error in an otherwise linear scale
| | NB No outliers
**Part (iii):** people heavier in $P$ than in $Q$; weights more spread out in $Q$ | B1 | Or equivalent statement
| B1 | 2 | Or equivalent statement
| | Cannot have two statements saying the equivalent of the same category (wts, spread, skewness). Must have the same statement relating to P and to Q.7 The weights in kilograms of two groups of 17-year-old males from country $P$ and country $Q$ are displayed in the following back-to-back stem-and-leaf diagram. In the third row of the diagram, ... $4 | 7 | 1 \ldots$ denotes weights of 74 kg for a male in country $P$ and 71 kg for a male in country $Q$.
\begin{center}
\begin{tabular}{|l|l|l|}
\hline
Country $P$ & & Country $Q$ \\
\hline
& 5 & 15 \\
\hline
& 6 & 2348 \\
\hline
98764 & 7 & 1345677889 \\
\hline
886653 & 8 & 2367788 \\
\hline
977655542 & 9 & 0224 \\
\hline
54431 & 10 & 45 \\
\hline
\end{tabular}
\end{center}
(i) Find the median and quartile weights for country $Q$.\\
(ii) You are given that the lower quartile, median and upper quartile for country $P$ are 84,94 and 98 kg respectively. On a single diagram on graph paper, draw two box-and-whisker plots of the data.\\
(iii) Make two comments on the weights of the two groups.
\hfill \mbox{\textit{CAIE S1 2002 Q7 [9]}}