| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Standard combined mean and SD |
| Difficulty | Moderate -0.8 This is a routine S1 question testing standard formulas for combining datasets. Students need to recall that combined mean = total sum/total n, and use the variance formula with Σx² values. It requires careful arithmetic but no problem-solving insight or novel approach—purely mechanical application of memorized formulas. |
| Spec | 2.02g Calculate mean and standard deviation |
| Answer | Marks | Guidance |
|---|---|---|
| \(\sum x = 12 \times 13 = 156\) | B1 | |
| \((\sum x^2)/12 - 13^2 = 10.2\) and \(\sum x^2 = 2150.4\) | M1 A1 | |
| For whole set, \(\sum x = 320\), \(\sum x^2 = 4522.4\) and Mean \(= 13.3\) | M1 A1 | |
| Variance \(= 4522.4 ÷ 24 - 13.3^2 = 10.7\) | M1 A1 A1 | 8 marks |
$\sum x = 12 \times 13 = 156$ | B1 |
$(\sum x^2)/12 - 13^2 = 10.2$ and $\sum x^2 = 2150.4$ | M1 A1 |
For whole set, $\sum x = 320$, $\sum x^2 = 4522.4$ and Mean $= 13.3$ | M1 A1 |
Variance $= 4522.4 ÷ 24 - 13.3^2 = 10.7$ | M1 A1 A1 | 8 marks\begin{enumerate}
\item Twelve observations are made of a random variable $X$. This set of observations has mean 13 and variance $10 \cdot 2$.
\end{enumerate}
Another twelve observations of $X$ are such that $\sum x = 164$ and $\sum x ^ { 2 } = 2372$.\\
Find the mean and the variance for all twenty-four observations.\\
\hfill \mbox{\textit{Edexcel S1 Q1 [8]}}