| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2002 |
| Session | January |
| Marks | 17 |
| 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 testing standard procedures: reading stem-and-leaf diagrams, finding median/quartiles, drawing box plots, and calculating mean/standard deviation. All parts follow textbook methods with no problem-solving or insight required—purely procedural recall and careful arithmetic. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Answer | Marks |
|---|---|
| \(Q_2 = 33\) | B1 |
| \(Q_1 = 27\); \(Q_3 = 51\) | B1 |
| \(\text{IQR} = 51 - 27 = 24\) | B1(3) |
| Answer | Marks |
|---|---|
| Boxplot | M1 |
| Labels | A1 |
| \(27, 33, 51\) | A1 (4) |
| A1 | |
| Boxplot with label | B (3) |
| Answer | Marks | Guidance |
|---|---|---|
| \(\mu = \frac{618}{15} = 41.2\) | M1 | \(\frac{\sum x}{15}\) |
| \(41.2\) correct as | A1 | |
| \(\sigma^2 = \frac{21864 - 41.2^2}{15}\) (Sq. Deviations = 21,38...) | M1 | \(\frac{\sum x^2}{15} - \mu^2\) |
| \(\sigma = 20.6597\)... | B1 only | |
| \(\Rightarrow\) \(\sigma \approx 20.7\) | A1 (5) |
| Answer | Marks | Guidance |
|---|---|---|
| Median male \(>\) Median female | B1 | Any two sensible |
| IQR male \(>\) IQR female etc. | B1 (2) | inferences using statistics |
| Males: skew stew; Females: slight \(+ve\)/almost symmetrical |
## Part (a)
$Q_2 = 33$ | B1 |
$Q_1 = 27$; $Q_3 = 51$ | B1 |
$\text{IQR} = 51 - 27 = 24$ | B1(3) |
## Part (b)
Boxplot | M1 |
Labels | A1 |
$27, 33, 51$ | A1 (4) |
| A1 |
Boxplot with label | B (3) |
## Part (c)
$\mu = \frac{618}{15} = 41.2$ | M1 | $\frac{\sum x}{15}$
$41.2$ correct as | A1 |
$\sigma^2 = \frac{21864 - 41.2^2}{15}$ (Sq. Deviations = 21,38...) | M1 | $\frac{\sum x^2}{15} - \mu^2$
$\sigma = 20.6597$... | B1 only |
$\Rightarrow$ $\sigma \approx 20.7$ | A1 (5) |
## Part (e)
Median male $>$ Median female | B1 | Any two sensible
IQR male $>$ IQR female etc. | B1 (2) | inferences using statistics
Males: skew stew; Females: slight $+ve$/almost symmetrical | |
---Hospital records show the number of babies born in a year. The number of babies delivered by 15 male doctors is summarised by the stem and leaf diagram below.
Babies \quad (4|5 means 45) \quad Totals
0 \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (0)
1|9 \quad \quad \quad \quad \quad \quad \quad \quad \quad (1)
2|1 6 7 7 \quad \quad \quad \quad \quad \quad (4)
3|2 2 3 4 8 \quad \quad \quad \quad \quad (5)
4|5 \quad \quad \quad \quad \quad \quad \quad \quad \quad (1)
5|1 \quad \quad \quad \quad \quad \quad \quad \quad \quad (1)
6|0 \quad \quad \quad \quad \quad \quad \quad \quad \quad (1)
7 \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad (0)
8|6 7 \quad \quad \quad \quad \quad \quad \quad \quad (2)
\begin{enumerate}[label=(\alph*)]
\item Find the median and inter-quartile range of these data. [3]
\item Given that there are no outliers, draw a box plot on graph paper to represent these data. Start your scale at the origin. [4]
\item Calculate the mean and standard deviation of these data. [5]
\end{enumerate}
The records also contain the number of babies delivered by 10 female doctors.
34 \quad 30 \quad 20 \quad 15 \quad 6
32 \quad 26 \quad 19 \quad 11 \quad 4
The quartiles are 11, 19.5 and 30.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{3}
\item Using the same scale as in part (b) and on the same graph paper draw a box plot for the data for the 10 female doctors. [3]
\item Compare and contrast the box plots for the data for male and female doctors. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2002 Q6 [17]}}