| Exam Board | AQA |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2012 |
| Session | January |
| Marks | 4 |
| 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 S1 question requiring basic application of median/quartile position formulas (n+1)/2 to grouped data with clear frequencies. Part (b) is simple conceptual understanding about open-ended classes. Significantly easier than average A-level maths questions. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Number of new potatoes | \(\leqslant 6\) | 7 | 8 | 9 | 10 | 11 | \(\geqslant 12\) |
| Frequency | 2 | 2 | 1 | 4 | 8 | 6 | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Median \(= 10\) | B1 | CAO |
| Upper quartile \(= 11\), Lower quartile \(= 9\) | B1 | CAO; either. May be implied by IQR \(= 2\) |
| Interquartile range \(= 2\) | B1 | CAO; do not award if seen to be not based on 11 and 9 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| Do not group results | B1 | OE statement implying non-grouping or recording of all separate observed values. Illustrations for B1: Use all values; Replace \(\leq 6\) by or use \((0), 1, ..., 6\); Replace \(\geq 12\) by or use \(12, 13, ...\); Record exact values/frequencies. Illustrations for B0: Record max and/or min values; Construct frequency table; Use \(1, 2\) or \(12, 13\) |
# Question 1:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Median $= 10$ | B1 | CAO |
| Upper quartile $= 11$, Lower quartile $= 9$ | B1 | CAO; either. May be implied by IQR $= 2$ |
| Interquartile range $= 2$ | B1 | CAO; do not award if seen to be not based on 11 and 9 |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| Do not group results | B1 | OE statement implying non-grouping or recording of all separate observed values. Illustrations for B1: Use all values; Replace $\leq 6$ by or use $(0), 1, ..., 6$; Replace $\geq 12$ by or use $12, 13, ...$; Record exact values/frequencies. Illustrations for B0: Record max and/or min values; Construct frequency table; Use $1, 2$ or $12, 13$ |
---1 Giles, a keen gardener, rents a council allotment.
During early April 2011, he planted 27 seed potatoes.
When he harvested his potato crop during the following August, he counted the number of new potatoes that he obtained from each seed potato.
He recorded his results as follows.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | }
\hline
Number of new potatoes & $\leqslant 6$ & 7 & 8 & 9 & 10 & 11 & $\geqslant 12$ \\
\hline
Frequency & 2 & 2 & 1 & 4 & 8 & 6 & 4 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate values for the median and the interquartile range of these data.
\item Advise Giles on how to record his corresponding data for 2012 so that it would then be possible to calculate the mean number of new potatoes per seed potato.
\end{enumerate}
\hfill \mbox{\textit{AQA S1 2012 Q1 [4]}}