| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Find median and quartiles from raw data list |
| Difficulty | Easy -1.8 This is a straightforward data handling question requiring only basic ordering of numbers and applying standard definitions of median, quartiles, and range. No problem-solving or conceptual understanding beyond recall of definitions is needed—significantly easier than average A-level questions. |
| Spec | 2.02f Measures of average and spread2.02h Recognize outliers |
| Answer | Marks | Guidance |
|---|---|---|
| Median = \(4.5\) (8th value) | B1 | Must be identified as 8th value |
| \(Q_1 = 3.85\) (average of 4th and 5th values) | M1 | Correct method for quartiles with \(n=15\) |
| \(Q_3 = 4.85\) (average of 12th and 13th values) | A1 | Both quartiles correct |
| \(IQR = 4.85 - 3.85 = 1.0\) | A1 | Correct IQR |
| Answer | Marks | Guidance |
|---|---|---|
| Range \(= 5.2 - 3.3 = 1.9\) | B1 | cao |
| Answer | Marks | Guidance |
|---|---|---|
| No value occurs more than once / all values are different / no repeated values | B1 | Accept equivalent statements indicating data has no repeated values |
# Question 1:
## Part (a) - Median and Interquartile Range [4 marks]
**Ordered data:**
3.3, 3.6, 3.7, 3.8, 3.9, 4.0, 4.1, **4.5**, 4.6, 4.7, 4.8, 4.9, 5.0, 5.1, 5.2
| Median = $4.5$ (8th value) | B1 | Must be identified as 8th value |
|---|---|---|
| $Q_1 = 3.85$ (average of 4th and 5th values) | M1 | Correct method for quartiles with $n=15$ |
| $Q_3 = 4.85$ (average of 12th and 13th values) | A1 | Both quartiles correct |
| $IQR = 4.85 - 3.85 = 1.0$ | A1 | Correct IQR |
## Part (b) - Range [1 mark]
| Range $= 5.2 - 3.3 = 1.9$ | B1 | cao |
## Part (c) - Mode not appropriate [1 mark]
| No value occurs more than once / all values are different / no repeated values | B1 | Accept equivalent statements indicating data has no repeated values |
---1 The weights, in kilograms, of a random sample of 15 items of cabin luggage on an aeroplane were as follows.
\section*{$\begin{array} { l l l l l l l l l l l l l l l } 4.6 & 3.8 & 3.9 & 4.5 & 4.9 & 3.6 & 3.7 & 5.2 & 4.0 & 5.1 & 4.1 & 3.3 & 4.7 & 5.0 & 4.8 \end{array}$}
For these data:
\begin{enumerate}[label=(\alph*)]
\item find values for the median and the interquartile range;
\item find the value for the range;
\item state why the mode is not an appropriate measure of average.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2014 Q1 [6]}}