| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| 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 routine S1 coding question requiring standard application of formulas to transform coded statistics back to original scale. While it involves multiple steps (calculating mean and SD of y, then decoding), these are mechanical applications of well-practiced techniques with no conceptual challenges or problem-solving required. |
| Spec | 2.02g Calculate mean and standard deviation5.02c Linear coding: effects on mean and variance |
| \(x\) | 75 | 80 | 85 | 90 | 95 | 100 | 105 | 110 |
| Frequency | 1 | 2 | 3 | 6 | 4 | 2 | 1 | 1 |
| Answer | Marks |
|---|---|
| \(Y\) values \(-3, -2, \ldots, 4\) | \(B1\) \(B1\) |
| \(\sum y = 5\), \(\sum y^2 = 57\) | |
| \(E(Y) = 5 + 20 = 0.25\) | \(M1\) \(A1\) |
| \(E(X) = 5E(Y) + 90 = 91.25\) | |
| \(\text{Var}(Y) = \frac{57}{20} - \frac{1}{16} = \frac{223}{80}\) | \(M1\) \(M1\) \(A1\) |
| \(\text{Var}(X) = 25 \text{ Var}(Y) = 69.7\) | |
| s.d. of \(Y = \sqrt{69.7} = 8.35\) | \(A1\) |
$Y$ values $-3, -2, \ldots, 4$ | $B1$ $B1$ |
$\sum y = 5$, $\sum y^2 = 57$ | |
$E(Y) = 5 + 20 = 0.25$ | $M1$ $A1$ |
$E(X) = 5E(Y) + 90 = 91.25$ | |
$\text{Var}(Y) = \frac{57}{20} - \frac{1}{16} = \frac{223}{80}$ | $M1$ $M1$ $A1$ |
$\text{Var}(X) = 25 \text{ Var}(Y) = 69.7$ | |
s.d. of $Y = \sqrt{69.7} = 8.35$ | $A1$ |
**Total: 8 marks**Using the coding $y = \frac{x-90}{5}$, and showing each step in your working clearly, calculate the mean and the standard deviation of the 20 observations of a variable $X$ given by the following table:
\begin{tabular}{|c|c|c|c|c|c|c|c|c|}
\hline
$x$ & 75 & 80 & 85 & 90 & 95 & 100 & 105 & 110 \\
\hline
Frequency & 1 & 2 & 3 & 6 & 4 & 2 & 1 & 1 \\
\hline
\end{tabular}
[8 marks]
\hfill \mbox{\textit{Edexcel S1 Q1 [8]}}