| Exam Board | CAIE |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | June |
| 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 a back-to-back stem-and-leaf diagram, finding median and IQR by counting positions, and drawing box plots. All techniques are routine for S1 with no problem-solving or conceptual challenges beyond careful counting. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| \(A\) | \(B\) | \multirow{3}{*}{(4)} | |
| 310 | 15 | 1335 | |
| 41 | 16 | 2234457778 | |
| 833 | 17 | 01333466799 | (11) |
| 988655432110 | 18 | 247 | (3) |
| 99886542 | 19 | 15 | (2) |
| 98710 | 20 | 4 | (1) |
| Answer | Marks | Guidance |
|---|---|---|
| (i) A: median = 0.186, IQ range = 0.198 − 0.179 = 0.019 | B1 | |
| M1 | Subt LQ from their UQ | |
| A1ft [3] | Correct IQ range ft dp in wrong place | |
| (ii) A (box plot shown with 2 correct boxes ft (i) OK if superimposed) | B1ft | |
| B (2 correct pairs whiskers lines up to box not inside) | B1 | |
| (scale from 0.15 to 0.21 shown with uniform scale) | B1 [3] | Correct uniform scale from at least 0.15 to 0.21 seen. No scale no marks (ii) unless perfect A and B with all 10 values shown |
(i) A: median = 0.186, IQ range = 0.198 − 0.179 = 0.019 | B1 |
| M1 | Subt LQ from their UQ
| A1ft [3] | Correct IQ range ft dp in wrong place
(ii) A (box plot shown with 2 correct boxes ft (i) OK if superimposed) | B1ft |
B (2 correct pairs whiskers lines up to box not inside) | B1 |
(scale from 0.15 to 0.21 shown with uniform scale) | B1 [3] | Correct uniform scale from at least 0.15 to 0.21 seen. No scale no marks (ii) unless perfect A and B with all 10 values shown4 The back-to-back stem-and-leaf diagram shows the values taken by two variables $A$ and $B$.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
$A$ & & $B$ & \multirow{3}{*}{(4)} \\
\hline
310 & 15 & 1335 & \\
\hline
41 & 16 & 2234457778 & \\
\hline
833 & 17 & 01333466799 & (11) \\
\hline
988655432110 & 18 & 247 & (3) \\
\hline
99886542 & 19 & 15 & (2) \\
\hline
98710 & 20 & 4 & (1) \\
\hline
\end{tabular}
\end{center}
Key: $4 | 16 | 7$ means $A = 0.164$ and $B = 0.167$.\\
(i) Find the median and the interquartile range for variable $A$.\\
(ii) You are given that, for variable $B$, the median is 0.171 , the upper quartile is 0.179 and the lower quartile is 0.164 . Draw box-and-whisker plots for $A$ and $B$ in a single diagram on graph paper.
\hfill \mbox{\textit{CAIE S1 2012 Q4 [6]}}