| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Coding to simplify calculation |
| Difficulty | Moderate -0.8 This is a straightforward S1 question testing basic statistical calculations (median, coded mean/SD, linear transformations of expectation). All parts follow standard algorithms with no problem-solving required—students simply apply memorized formulas. The coding simplifies arithmetic but adds no conceptual challenge. Easier than average A-level maths. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation5.02c Linear coding: effects on mean and variance |
| Answer | Marks |
|---|---|
| (a) \(M = (94 + 106) \div 2 = 100\) | B1 |
| (b) \(y\) values: \(-20, -17, -12, -10, -3, 3, 5, 8, 12, 20\) | B1 |
| \(E(Y) = -1.4\), so \(E(X) = 2(-1.4) + 100 = 97.2\) | M1 A1 |
| s.d. of \(Y = \sqrt{156.44} = 12.5\), so s.d. of \(X = 25.0\) | M1 A1 A1 |
| (c) \(E(3X - 5) = 3(97.2) - 5 = 286.6\) | M1 A1 A1 |
| 10 marks total |
(a) $M = (94 + 106) \div 2 = 100$ | B1 |
(b) $y$ values: $-20, -17, -12, -10, -3, 3, 5, 8, 12, 20$ | B1 |
$E(Y) = -1.4$, so $E(X) = 2(-1.4) + 100 = 97.2$ | M1 A1 |
s.d. of $Y = \sqrt{156.44} = 12.5$, so s.d. of $X = 25.0$ | M1 A1 A1 |
(c) $E(3X - 5) = 3(97.2) - 5 = 286.6$ | M1 A1 A1 |
| 10 marks total |The variable $X$ represents the marks out of 150 scored by a group of students in an examination. The following ten values of $X$ were obtained:
60, 66, 76, 80, 94, 106, 110, 116, 124, 140.
\begin{enumerate}[label=(\alph*)]
\item Write down the median, $M$, of the ten marks. [1 mark]
\item Using the coding $y = \frac{x - M}{2}$, and showing all your working clearly, find the mean and the standard deviation of the marks. [6 marks]
\item Find E$(3X - 5)$. [3 marks]
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [10]}}