| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2010 |
| Session | January |
| Marks | 9 |
| 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 straightforward S1 question testing basic statistical measures from a stem-and-leaf diagram. Parts (a) and (b) require simple counting to find median and quartiles with n=19. Part (c) applies a given outlier formula (no derivation needed), and part (d) is routine box plot construction. All steps are standard textbook procedures with no problem-solving or conceptual challenge. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread2.02h Recognize outliers |
| Answer | Marks |
|---|---|
| Marks: B1 | (1) |
| Answer | Marks |
|---|---|
| Marks: B1 B1 B1ft | (3) |
| Answer | Marks |
|---|---|
| Marks: M1 A1ft | (2) |
| Answer | Marks |
|---|---|
| Marks: B1ft B1 B1ft | (3) |
## Part (a)
**Answer:** Median is 33
**Marks:** B1 | (1)
## Part (b)
**Answer:** $Q_1 = 24$, $Q_3 = 40$, $\text{IQR} = 16$
**Marks:** B1 B1 B1ft | (3)
**Guidance:**
- 1st B1 for $Q_1 = 24$
- 2nd B1 for $Q_3 = 40$
- 3rd B1ft for their IQR based on their lower and upper quartile. Calculation of range (40 – 7 = 33) is B0B0B0
## Part (c)
**Answer:** $Q_1 - \text{IQR} \times 24 - 16 = 8$. So 7 is only outlier
**Marks:** M1 A1ft | (2)
**Guidance:**
- M1 for evidence that $Q_1 - \text{IQR}$ has been attempted, their "8" (>7) seen or clearly attempted is sufficient
- A1ft must have seen their "8" and a suitable comment that only one person scored below this
## Part (d)
**Answer:** Box plot with correct shape with:
- Box clearly marked at approximately 24, 33, 40 readable off the scale
- Lower whisker to 7
- Upper whisker (accept either whisker)
**Marks:** B1ft B1 B1ft | (3)
**Guidance:**
- 1st B1ft for a clear box shape and fit their $Q_1$, $Q_2$ and $Q_3$ readable off the scale. Allow this mark for a box shape even if $Q_1 = 40$, $Q_3 = 7$ and $Q_2 = 33$ are used
- 2nd B1 for only one outlier appropriately marked at 7
- 3rd B1ft for either lower whisker. If they choose the whisker to their lower limit for outliers then follow through their "8". (There should be no upper whisker unless their $Q_3 < 40$, in which case there should be a whisker to 40)
- A typical error in (d) is to draw the lower whisker to 7, this can only score B1B0B0
---The 19 employees of a company take an aptitude test. The scores out of 40 are illustrated in the stem and leaf diagram below.
$2|6$ means a score of 26
\begin{align}
0 & | 7 & (1) \\
1 & | 88 & (2) \\
2 & | 4468 & (4) \\
3 & | 2333459 & (7) \\
4 & | 00000 & (5)
\end{align}
Find
\begin{enumerate}[label=(\alph*)]
\item the median score, [1]
\item the interquartile range. [3]
\end{enumerate}
The company director decides that any employees whose scores are so low that they are outliers will undergo retraining.
An outlier is an observation whose value is less than the lower quartile minus 1.0 times the interquartile range.
\begin{enumerate}[label=(\alph*), start=3]
\item Explain why there is only one employee who will undergo retraining. [2]
\item On the graph paper on page 5, draw a box plot to illustrate the employees' scores. [3]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 2010 Q2 [9]}}