| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 14 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from stem-and-leaf diagram |
| Difficulty | Easy -1.2 This is a routine S1 statistics question requiring straightforward counting from a stem-and-leaf diagram, finding median/quartiles using standard position formulas, and applying the given outlier formula. All techniques are mechanical with no problem-solving or conceptual insight required—easier than average A-level. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02h Recognize outliers |
| Number of months | (2 | 1 means 21 months) | Totals | |
| 0 | 11224446779 | (11) | |
| 1 | 02355689 | ( ) | |
| 2 | 1568 | ( ) | |
| 3 | 079 | ( ) | |
| 4 | 5 | ( ) | |
| 5 | 27 | (2) | |
| 6 | 3 | (1) | |
| 7 | 0 | (1) |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(8, 4, 3, 1\) | A1 | |
| (b) \(4\) months | A1 | |
| (c) \(n = 31\); \(Q_1 = 8^{\text{th}} = 6\) months | M1 A1 | |
| A1 | ||
| \(Q_2 = 16^{\text{th}} = 15\) months | A1 | |
| \(Q_3 = 24^{\text{th}} = 30\) months | A1 | |
| (d) \(Q_3 - Q_1 = 30 - 6 = 24\) | M1 | |
| limits are \(6 - (1.5 \times 24) = -30\) and \(30 + (1.5 \times 24) = 66\) | M1 | |
| \(\therefore\) 70 is an outlier | A1 | |
| (e) [Boxplot shown with whiskers at approximately 0 and 60, box from 6 to 30, median at 15, outlier marked at 70] | B3 | |
| (f) +ve skew | B1 | |
| e.g. lot of people unemployed for a short time, only a few for a long time | B1 | (14) |
(a) $8, 4, 3, 1$ | A1 |
(b) $4$ months | A1 |
(c) $n = 31$; $Q_1 = 8^{\text{th}} = 6$ months | M1 A1 |
| A1 |
$Q_2 = 16^{\text{th}} = 15$ months | A1 |
$Q_3 = 24^{\text{th}} = 30$ months | A1 |
(d) $Q_3 - Q_1 = 30 - 6 = 24$ | M1 |
limits are $6 - (1.5 \times 24) = -30$ and $30 + (1.5 \times 24) = 66$ | M1 |
$\therefore$ 70 is an outlier | A1 |
(e) [Boxplot shown with whiskers at approximately 0 and 60, box from 6 to 30, median at 15, outlier marked at 70] | B3 |
(f) +ve skew | B1 |
e.g. lot of people unemployed for a short time, only a few for a long time | B1 | (14)5. In a survey unemployed people were asked how many months it had been, to the nearest month, since they were last employed on a full-time basis. The data collected is summarised in this stem and leaf diagram.
\begin{center}
\begin{tabular}{|l|l|l|l|}
\hline
Number of months & & (2 | 1 means 21 months) & Totals \\
\hline
0 & & 11224446779 & (11) \\
\hline
1 & & 02355689 & ( ) \\
\hline
2 & 1568 & & ( ) \\
\hline
3 & 079 & & ( ) \\
\hline
4 & 5 & & ( ) \\
\hline
5 & 27 & & (2) \\
\hline
6 & 3 & & (1) \\
\hline
7 & 0 & & (1) \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Write down the values needed to complete the totals column on the stem and leaf diagram.
\item State the mode of these data.
\item Find the median and quartiles of these data.
Given that any values outside of the limits $\mathrm { Q } _ { 1 } - 1.5 \left( \mathrm { Q } _ { 3 } - \mathrm { Q } _ { 1 } \right)$ and $\mathrm { Q } _ { 3 } + 1.5 \left( \mathrm { Q } _ { 3 } - \mathrm { Q } _ { 1 } \right)$ are to be regarded as outliers,
\item determine if there are any outliers in these data,
\item draw a box plot representing these data on graph paper,
\item describe the skewness of these data and suggest a reason for it.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q5 [14]}}