| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from grouped frequency table |
| Difficulty | Moderate -0.3 This is a standard S1 grouped frequency question requiring routine calculations of mean and standard deviation using midpoints, followed by straightforward interpretation about skewness. The calculations are mechanical (though tedious with unequal class widths), and parts (b)-(c) test basic understanding that skewed data favors median/IQR over mean/SD—a core syllabus point with minimal problem-solving demand. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| \(m\) (minutes) | Number of teams |
| \(0 \leq m < 40\) | 36 |
| \(40 \leq m < 80\) | 28 |
| \(80 \leq m < 120\) | 10 |
| \(120 \leq m < 160\) | 4 |
| \(160 \leq m < 200\) | 5 |
| \(200 \leq m < 300\) | 4 |
| \(300 \leq m < 400\) | 2 |
| \(400 \leq m < 600\) | 3 |
| Answer | Marks | Guidance |
|---|---|---|
| midpoints: \(20, 60, 100, 140, 180, 250, 350, 500\) | M1 | |
| A1 | ||
| \(\text{mean} = \frac{8060}{92} = 87.6\) (3sf) | M1 A1 | |
| \(\sum fm^2 = 1\,700\,600\) | A1 | |
| \(\text{std. dev.} = \sqrt{\frac{1\,700\,600}{92} - (87.609)^2} = 104\) (3sf) | M2 A1 | |
| e.g. data very skewed, mean and std. dev. strongly affected by a few very large values | B2 | |
| e.g. median and IQR | B1 | (11) |
midpoints: $20, 60, 100, 140, 180, 250, 350, 500$ | M1 |
| A1 |
$\text{mean} = \frac{8060}{92} = 87.6$ (3sf) | M1 A1 |
$\sum fm^2 = 1\,700\,600$ | A1 |
$\text{std. dev.} = \sqrt{\frac{1\,700\,600}{92} - (87.609)^2} = 104$ (3sf) | M2 A1 |
e.g. data very skewed, mean and std. dev. strongly affected by a few very large values | B2 |
e.g. median and IQR | B1 | (11)3. A soccer fan collected data on the number of minutes of league football, $m$, played by each team in the four main divisions before first scoring a goal at the start of a new season. Her results are shown in the table below.
\begin{center}
\begin{tabular}{|l|l|}
\hline
$m$ (minutes) & Number of teams \\
\hline
$0 \leq m < 40$ & 36 \\
\hline
$40 \leq m < 80$ & 28 \\
\hline
$80 \leq m < 120$ & 10 \\
\hline
$120 \leq m < 160$ & 4 \\
\hline
$160 \leq m < 200$ & 5 \\
\hline
$200 \leq m < 300$ & 4 \\
\hline
$300 \leq m < 400$ & 2 \\
\hline
$400 \leq m < 600$ & 3 \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Calculate estimates of the mean and standard deviation of these data.
\item Explain why the mean and standard deviation might not be the best summary statistics to use with these data.
\item Suggest alternative summary statistics that would better represent these data.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [11]}}