| Exam Board | SPS |
|---|---|
| Module | SPS FM Statistics (SPS FM Statistics) |
| Year | 2021 |
| Session | June |
| Marks | 4 |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from grouped frequency table |
| Difficulty | Moderate -0.8 This is a straightforward grouped data mean calculation requiring students to set up and solve a linear equation using midpoint values. It involves standard GCSE/AS-level statistical techniques with no conceptual challenges—just careful arithmetic and algebraic manipulation. |
| Spec | 2.02g Calculate mean and standard deviation |
| Time taken (\(t\) minutes) | Number of people |
| \(0 < t \leq 10\) | \(x\) |
| \(10 < t \leq 20\) | 30 |
| \(20 < t \leq 30\) | 35 |
| \(30 < t \leq 50\) | 28 |
| \(50 < t \leq 90\) | 12 |
Employees at a company were asked how long their average commute to work was. The table below gives information about their answers.
\begin{tabular}{|c|c|}
\hline
Time taken ($t$ minutes) & Number of people \\
\hline
$0 < t \leq 10$ & $x$ \\
\hline
$10 < t \leq 20$ & 30 \\
\hline
$20 < t \leq 30$ & 35 \\
\hline
$30 < t \leq 50$ & 28 \\
\hline
$50 < t \leq 90$ & 12 \\
\hline
\end{tabular}
The company estimates that the mean time for employees commuting to work is 28 minutes. Work out the value of $x$, showing your working clearly.
[4]
\hfill \mbox{\textit{SPS SPS FM Statistics 2021 Q1 [4]}}