| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from raw data |
| Difficulty | Moderate -0.8 This is a straightforward S1 question requiring standard calculations of summary statistics from given data and applying linear transformations. The median requires simple counting, mean and standard deviation use provided sums with standard formulas, and part (b) applies well-known transformation rules. All techniques are routine textbook exercises with no problem-solving or conceptual challenges. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| 5 | 19 | 20 | 21 | 23 | 25 | 31 | 37 | 39 | 41 |
| 42 | 44 | 47 | 51 | 56 | 57 | 60 | 61 | 62 | 65 |
| 67 | 70 | 71 | 73 | 75 | 77 | 81 | 82 | 98 | 100 |
| Answer | Marks | Guidance |
|---|---|---|
| (a) Median = \(56.5\) | B1 B1 | |
| Mean = \(\frac{1600}{30} = 53\frac{1}{3}\) | M1 A1 A1 | |
| Var = \(\frac{102400}{30} - \left(\frac{1600}{30}\right)^2 = 568.89\), so s.d. = \(23.9\) | ||
| (b) Median = \(65.2\), mean = \(62\frac{2}{3}\), variance = \(0.8 \times 23.9 = 19.1\) | B1 B1 M1 A1 | Total: 9 marks |
(a) Median = $56.5$ | B1 B1 |
Mean = $\frac{1600}{30} = 53\frac{1}{3}$ | M1 A1 A1 |
Var = $\frac{102400}{30} - \left(\frac{1600}{30}\right)^2 = 568.89$, so s.d. = $23.9$ |
(b) Median = $65.2$, mean = $62\frac{2}{3}$, variance = $0.8 \times 23.9 = 19.1$ | B1 B1 M1 A1 | **Total: 9 marks**4. The marks, $x$ out of 100 , scored by 30 candidates in an examination were as follows:
\begin{center}
\begin{tabular}{ | r r r r r r r r r r | }
\hline
5 & 19 & 20 & 21 & 23 & 25 & 31 & 37 & 39 & 41 \\
42 & 44 & 47 & 51 & 56 & 57 & 60 & 61 & 62 & 65 \\
67 & 70 & 71 & 73 & 75 & 77 & 81 & 82 & 98 & 100 \\
\hline
\end{tabular}
\end{center}
Given that $\sum x = 1600$ and $\sum x ^ { 2 } = 102400$,
\begin{enumerate}[label=(\alph*)]
\item find the median, the mean and the standard deviation of these marks.
The marks were scaled to give modified scores, $y$, using the formula $y = \frac { 4 x } { 5 } + 20$.
\item Find the median, the mean and the standard deviation of the modified scores.
\section*{STATISTICS 1 (A) TEST PAPER 1 Page 2}
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q4 [9]}}