| Exam Board | WJEC |
|---|---|
| Module | Unit 2 (Unit 2) |
| Year | 2024 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from grouped frequency table |
| Difficulty | Easy -1.2 This is a statistics question requiring interpretation of graphs/data and basic calculations (mean, standard deviation from grouped frequency table with given Σx²f). Part (a) tests critical reading of statistics in media (1 mark), parts (b)(i) uses standard formulas with straightforward arithmetic (4 marks), other parts require simple observations. All techniques are routine A-level statistics content with no problem-solving or novel insight required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation2.02i Select/critique data presentation |
| Daily number | Midpoint | Frequency | Percentage |
| of 2nd dose | \(x\) | \(f\) | |
| vaccines | |||
| (1000s) | |||
| \(0 \leqslant v < 100\) | 50 | 2 | 3·3 |
| \(100 \leqslant v < 200\) | 150 | 8 | 13·1 |
| \(200 \leqslant v < 300\) | 250 | 10 | 16·4 |
| \(300 \leqslant v < 400\) | 350 | 13 | 21·3 |
| \(400 \leqslant v < 500\) | 450 | 26 | 42·6 |
| \(500 \leqslant v < 600\) | 550 | 2 | 3·3 |
| Total | 61 | 100 |
In March 2020, the coronavirus pandemic caused major disruption to the lives of individuals across the world. A newspaper published the following graph from the gov.uk website, along with an article which included the following excerpt.
"The daily number of vaccines administered continues to fall. In order to get control of the virus, we need the number of people receiving a second dose of the vaccine to keep rocketing. The fear is it will start to drop off soon, which will leave many people still unprotected."
\includegraphics{figure_5}
\begin{enumerate}[label=(\alph*)]
\item By referring to the graph, explain how the quote could be misleading. [1]
\end{enumerate}
The daily numbers of second dose vaccines, in thousands, over the period April 1st 2021 to May 31st 2021 are shown in the table below.
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
\textbf{Daily number} & \textbf{Midpoint} & \textbf{Frequency} & \textbf{Percentage} \\
\textbf{of 2nd dose} & $x$ & $f$ & \\
\textbf{vaccines} & & & \\
\textbf{(1000s)} & & & \\
\hline
$0 \leqslant v < 100$ & 50 & 2 & 3·3 \\
$100 \leqslant v < 200$ & 150 & 8 & 13·1 \\
$200 \leqslant v < 300$ & 250 & 10 & 16·4 \\
$300 \leqslant v < 400$ & 350 & 13 & 21·3 \\
$400 \leqslant v < 500$ & 450 & 26 & 42·6 \\
$500 \leqslant v < 600$ & 550 & 2 & 3·3 \\
\hline
Total & & 61 & 100 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]\setcounter{enumi}{1}
\item \begin{enumerate}[label=(\roman*)]
\item Calculate estimates of the mean and standard deviation for the daily number of second dose vaccines given over this period. You may use $\sum x^2 f = 8272500$. [4]
\item Comment on the skewness of these data. [1]
\end{enumerate}
\item Give a possible reason for the pattern observed in this graph. [1]
\item State, with a reason, whether or not you think the data for April 15th to April 18th are incorrect. [1]
\end{enumerate}
\hfill \mbox{\textit{WJEC Unit 2 2024 Q5 [8]}}