| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2004 |
| Session | November |
| Marks | 14 |
| 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 S1 question requiring basic stem-and-leaf reading skills and standard quartile calculations. Finding quartiles from ordered data and identifying outliers using the given formula are routine procedures. The box plot drawing and skewness comment require only direct observation of the given statistics, with no problem-solving or novel insight needed. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| Totals | Asif | Totals | |||||||||||||||||
| (9) | 8 | 7 | 4 | 3 | 2 | 1 | 1 | 0 | 18 | 4 | 4 | 5 | 7 | (4) | |||||
| (11) | 9 | 8 | 6 | 5 | 4 | 3 | 3 | 1 | 1 | 19 | 5 | 7 | 8 | 9 | 9 | (5) | |||
| (6) | 8 | 7 | 4 | 2 | 2 | 0 | 20 | 0 | 2 | 2 | 4 | 4 | 8 | (6) | |||||
| (6) | 9 | 4 | 3 | 1 | 0 | 0 | 21 | 2 | 3 | 5 | 6 | 6 | 7 | 9 | (7) | ||||
| (4) | 6 | 4 | 1 | 1 | 22 | 1 | 1 | 2 | 4 | 5 | 5 | 8 | (7) | ||||||
| (2) | 2 | 0 | 23 | 1 | 1 | 3 | 4 | 6 | 6 | 7 | 8 | (8) | |||||||
| (2) | 7 | 1 | 24 | 2 | 4 | 8 | 9 | (4) | |||||||||||
| (1) | 9 | 25 | 4 | (1) | |||||||||||||||
| (2) | 9 | 3 | 26 | (0) | |||||||||||||||
| Keith | Asif | |
| Lower quartile | 191 | \(a\) |
| Median | \(b\) | 218 |
| Upper quartile | 221 | \(c\) |
\begin{enumerate}
\item As part of their job, taxi drivers record the number of miles they travel each day. A random sample of the mileages recorded by taxi drivers Keith and Asif are summarised in the back-toback stem and leaf diagram below.
\end{enumerate}
\begin{center}
\begin{tabular}{|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|l|}
\hline
Totals & \multicolumn{2}{|c|}{} & & & & \multicolumn{5}{|c|}{} & \multicolumn{2}{|c|}{} & \multicolumn{3}{|r|}{Asif} & \multicolumn{3}{|c|}{} & Totals \\
\hline
(9) & & 8 & 7 & 4 & 3 & 2 & 1 & 1 & 0 & 18 & 4 & 4 & 5 & 7 & & & & & (4) \\
\hline
(11) & 9 & 8 & 6 & 5 & 4 & 3 & 3 & 1 & 1 & 19 & 5 & 7 & 8 & 9 & 9 & & & & (5) \\
\hline
(6) & & & & 8 & 7 & 4 & 2 & 2 & 0 & 20 & 0 & 2 & 2 & 4 & 4 & 8 & & & (6) \\
\hline
(6) & & & & 9 & 4 & 3 & 1 & 0 & 0 & 21 & 2 & 3 & 5 & 6 & 6 & 7 & 9 & & (7) \\
\hline
(4) & & & & & & 6 & 4 & 1 & 1 & 22 & 1 & 1 & 2 & 4 & 5 & 5 & 8 & & (7) \\
\hline
(2) & & & & & & & & 2 & 0 & 23 & 1 & 1 & 3 & 4 & 6 & 6 & 7 & 8 & (8) \\
\hline
(2) & & & & & & & & 7 & 1 & 24 & 2 & 4 & 8 & 9 & & & & & (4) \\
\hline
(1) & & & & & & & & & 9 & 25 & 4 & & & & & & & & (1) \\
\hline
(2) & & & & & & & & 9 & 3 & 26 & & & & & & & & & (0) \\
\hline
\end{tabular}
\end{center}
Key: 0184 means 180 for Keith and 184 for Asif\\
The quartiles for these two distributions are summarised in the table below.
\begin{center}
\begin{tabular}{ | l | c | c | }
\hline
& Keith & Asif \\
\hline
Lower quartile & 191 & $a$ \\
\hline
Median & $b$ & 218 \\
\hline
Upper quartile & 221 & $c$ \\
\hline
\end{tabular}
\end{center}
(a) Find the values of $a , b$ and $c$.
Outliers are values that lie outside the limits
$$Q _ { 1 } - 1.5 \left( Q _ { 3 } - Q _ { 1 } \right) \text { and } Q _ { 3 } + 1.5 \left( Q _ { 3 } - Q _ { 1 } \right) .$$
(b) On graph paper, and showing your scale clearly, draw a box plot to represent Keith's data.\\
(c) Comment on the skewness of the two distributions.\\
\hfill \mbox{\textit{Edexcel S1 2004 Q1 [14]}}