| Exam Board | AQA |
|---|---|
| Module | Further AS Paper 2 Statistics (Further AS Paper 2 Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Compare multiple measures numerically |
| Difficulty | Easy -1.2 This is a straightforward discrete probability distribution question requiring only basic recall of definitions (mode, median) and a simple expected value calculation. The multi-part structure and context add minimal complexity—each part is routine with no problem-solving or insight required. |
| Spec | 2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Modal score \(= 10\) | B1 | States correct modal score |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(\begin{array}{c | c | c |
| Median score \(= 5\) | A1 | Obtains correct median score |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Mean score \(= 0 \times 0.25 + 5 \times 0.3 + 10 \times 0.35 + 20 \times 0.1 = 7\) | M1 | Uses formula for mean of a discrete random variable to calculate mean score or adjusts model to directly model prize money |
| Mean prize money \(= 7 \times 100 = £700\) | A1 | Obtains correct mean prize money |
## Question 5(a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Modal score $= 10$ | B1 | States correct modal score |
## Question 5(b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $\begin{array}{c|c|c|c|c} x & 0 & 5 & 10 & 20 \\ \hline P(X \leq x) & 0.25 & 0.55 & 0.9 & 1 \end{array}$ | M1 | Models the situation with a discrete random variable |
| Median score $= 5$ | A1 | Obtains correct median score |
## Question 5(c):
| Answer/Working | Mark | Guidance |
|---|---|---|
| Mean score $= 0 \times 0.25 + 5 \times 0.3 + 10 \times 0.35 + 20 \times 0.1 = 7$ | M1 | Uses formula for mean of a discrete random variable to calculate mean score or adjusts model to directly model prize money |
| Mean prize money $= 7 \times 100 = £700$ | A1 | Obtains correct mean prize money |
---5 In a game it is known that:
\begin{itemize}
\item 25\% of players score 0
\item 30\% of players score 5
\item 35\% of players score 10
\item 10\% of players score 20
\end{itemize}
Players receive prize money, in pounds, equal to 100 times their score.\\
5
\begin{enumerate}[label=(\alph*)]
\item State the modal score.\\[0pt]
[1 mark]
5
\item Find the median score.\\
5
\item Find the mean prize money received by a player.
\end{enumerate}
\hfill \mbox{\textit{AQA Further AS Paper 2 Statistics 2021 Q5 [5]}}