| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2018 |
| Session | October |
| Marks | 11 |
| 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 -1.3 This is a straightforward S1 question requiring routine application of standard procedures: reading values from a stem-and-leaf diagram, finding median/quartiles using position formulas for n=33, applying the given outlier formula, and drawing a box plot. All techniques are direct recall with no problem-solving or conceptual challenge beyond basic data handling. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02h Recognize outliers |
| 3 | 2 | 3 | 7 | ||||||||||||
| 4 | 1 | 3 | 3 | 4 | 5 | 5 | 6 | 9 | |||||||
| 5 | 1 | 2 | 2 | 3 | 4 | 4 | 5 | 5 | 5 | 7 | 8 | 8 | 9 | 9 | 9 |
| 6 | 2 | 3 | 3 | ||||||||||||
| 7 | 1 | 4 | 7 | ||||||||||||
| 8 | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(Q_2 = 54\), \(Q_1 = 45\), \(Q_3 = 59\) | B1, B1, B1 (3) | |
| (b) Upper limit \(= 59 + 1.5 \times 14 = 80\) | M1 | Correct expression for either limit ft their values in (a) |
| Lower limit \(= 45 - 1.5 \times 14 = 24\) | A1 | |
| Outlier 84 | A1ft | All outliers identified using their limits (must be stated in (b)) |
| (3) | ||
| (c) [Box plot showing whiskers on both sides, with \(Q_2\) and quartiles fitted from (a), two whiskers on RHS] | B1, B1, B1 (3) | 1st B1: Box with whiskers drawn and \(Q_2\) and quartiles ft from (a), condone 2 whiskers on RHS. 2nd B1: For only one lower whisker to 32 and no outliers. 3rd B1: For upper whisker to 80 or 77 and an outlier at 84. NB: If there are whiskers at both 77 and 80 it is 3rd B0 |
| (d) Any two from: The females are heavier than the males (on average). / The males have lower median than females. / The males have a smaller IQR than the females. / The females have a greater range than males. [Comments just about skewness are B0] | B1, B1 (2) | 1st B1: a correct comparison on location e.g. median or comment implying "on average". 2nd B1: a second correct comparison on spread e.g. range or IQR (greater spread is B0) |
| Total 11 |
**(a)** $Q_2 = 54$, $Q_1 = 45$, $Q_3 = 59$ | B1, B1, B1 (3) |
**(b)** Upper limit $= 59 + 1.5 \times 14 = 80$ | M1 | Correct expression for either limit ft their values in (a)
| Lower limit $= 45 - 1.5 \times 14 = 24$ | A1 |
| Outlier 84 | A1ft | All outliers identified using their limits (must be stated in (b))
| | (3) |
**(c)** [Box plot showing whiskers on both sides, with $Q_2$ and quartiles fitted from (a), two whiskers on RHS] | B1, B1, B1 (3) | 1st B1: Box with whiskers drawn and $Q_2$ and quartiles ft from (a), condone 2 whiskers on RHS. 2nd B1: For only one lower whisker to 32 and no outliers. 3rd B1: For upper whisker to 80 or 77 and an outlier at 84. NB: If there are whiskers at both 77 and 80 it is 3rd B0
**(d)** Any two from: The females are heavier than the males (on average). / The males have lower median than females. / The males have a smaller IQR than the females. / The females have a greater range than males. [Comments just about skewness are B0] | B1, B1 (2) | 1st B1: a correct comparison on location e.g. median or comment implying "on average". 2nd B1: a second correct comparison on spread e.g. range or IQR (greater spread is B0)
| | **Total 11** |
---\begin{enumerate}
\item The weights, to the nearest kilogram, of a sample of 33 female spotted hyenas living in the Serengeti are summarised in the stem and leaf diagram below.
\end{enumerate}
\begin{table}[h]
\begin{center}
\captionsetup{labelformat=empty}
\caption{Weight (kg)}
\begin{tabular}{ l | l l l l l l l l l l l l l l l }
3 & 2 & 3 & 7 & & & & & & & & & & & & \\
4 & 1 & 3 & 3 & 4 & 5 & 5 & 6 & 9 & & & & & & & \\
5 & 1 & 2 & 2 & 3 & 4 & 4 & 5 & 5 & 5 & 7 & 8 & 8 & 9 & 9 & 9 \\
6 & 2 & 3 & 3 & & & & & & & & & & & & \\
7 & 1 & 4 & 7 & & & & & & & & & & & & \\
8 & 4 & & & & & & & & & & & & & & \\
\end{tabular}
\end{center}
\end{table}
Totals\\
(a) Find the median and quartiles for the weights of the female spotted hyenas.
An outlier is defined as any value greater than $c$ or any value less than $d$ where
$$\begin{aligned}
& c = Q _ { 3 } + 1.5 \left( Q _ { 3 } - Q _ { 1 } \right) \\
& d = Q _ { 1 } - 1.5 \left( Q _ { 3 } - Q _ { 1 } \right)
\end{aligned}$$
(b) Showing your working clearly, identify any outliers for these data.\\
(3)
The weights, to the nearest kilogram, of a sample of male spotted hyenas living in the Serengeti are summarised below.\\
\includegraphics[max width=\textwidth, alt={}, center]{0377c6e9-ab4f-477d-9236-0732fe81f25e-06_755_1568_1537_185}\\
(c) In the space provided in the grid above, draw a box and whisker plot to represent the weights of female spotted hyenas living in the Serengeti. Indicate clearly any outliers. (A copy of this grid is on page 9 if you need to redraw your box and whisker plot.)\\
(d) Compare the weights of male and female spotted hyenas living in the Serengeti.
Key: 3|2 means 32
\begin{center}
\end{center}
\includegraphics[max width=\textwidth, alt={}, center]{0377c6e9-ab4f-477d-9236-0732fe81f25e-09_2658_101_107_9}\\
\hfill \mbox{\textit{Edexcel S1 2018 Q2 [11]}}