| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2020 |
| Session | October |
| Marks | 9 |
| Topic | Data representation |
| Type | Complete frequency table and histogram together |
| Difficulty | Standard +0.3 This is a standard histogram/frequency table question requiring frequency density calculations, mean estimation from grouped data, and quartile work. All techniques are routine A-level statistics procedures with no novel problem-solving required. The multi-part structure and 9 marks suggest slightly above trivial difficulty, but each part follows textbook methods directly. |
| Spec | 2.02b Histogram: area represents frequency2.02f Measures of average and spread2.02h Recognize outliers |
| Time, \(t\) (minutes) | \(5 < t \leq 7\) | \(7 < t \leq 10\) | \(10 < t \leq 14\) | \(14 < t \leq 18\) | \(18 < t \leq 30\) |
| Frequency | 10 | 23 | 51 |
7. The partially completed table below summarises the times taken by 120 job applicants to complete a task.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | }
\hline
Time, $t$ (minutes) & $5 < t \leq 7$ & $7 < t \leq 10$ & $10 < t \leq 14$ & $14 < t \leq 18$ & $18 < t \leq 30$ \\
\hline
Frequency & 10 & 23 & 51 & & \\
\hline
\end{tabular}
\end{center}
A histogram is drawn. The bar representing the $5 < t \leq 7$ has a width of 1 cm and a height of 5 cm .
\begin{enumerate}[label=(\alph*)]
\item Given that the bar representing the group $14 < t \leq 18$ has a height of 4 cm , find the frequency of this group.\\
(2)
\item Showing your working, estimate the mean time taken by the 120 job applicants.\\
(3)
The lower quartile of the times is 9.6 minutes and the upper quartile of the times is 15.5 minutes.\\
For these data, an outlier is classified as any value greater than $Q _ { 3 } + 1.5 \times$ IQR .
\item Showing your working, explain whether or not any of the times taken by these 120 job applicants might be classified as outliers.\\
(2)
Candidates with the fastest $5 \%$ of times for the task are given interviews.
\item Estimate the time taken by a job applicant, below which they might be given an interview.\\
(2)
\end{enumerate}
\hfill \mbox{\textit{SPS SPS FM Statistics 2020 Q7 [9]}}