| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Removing data values |
| Difficulty | Moderate -0.8 This is a straightforward S1 statistics question requiring standard formula application for mean and variance from summary statistics, followed by conceptual understanding of how removing/replacing a data value affects these measures. Part (a) is direct substitution into formulas (Σw/n and Σw²/n - mean²), while part (b) tests basic understanding that replacing a heavier value with a lighter one decreases the mean and affects variance predictably. No complex problem-solving or novel insight required—typical textbook exercise below average difficulty. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Answer | Marks |
|---|---|
| mean = \(\frac{1145.3}{15} = 76.4\) kg | M1 A1 |
| variance = \(\frac{8804.14}{15} - 76.353^2 = 39.6\) kg\(^2\) | M2 A1 |
| Answer | Marks |
|---|---|
| mean lower as replacement weighs less | B2 |
| variance higher as replacement's weight further from mean | B2 |
| (9) |
**Part (a)**
mean = $\frac{1145.3}{15} = 76.4$ kg | M1 A1 |
variance = $\frac{8804.14}{15} - 76.353^2 = 39.6$ kg$^2$ | M2 A1 |
**Part (b)**
mean lower as replacement weighs less | B2 |
variance higher as replacement's weight further from mean | B2 |
| (9) |\begin{enumerate}
\item The weight in kilograms, $w$, of the 15 players in a rugby team was recorded and the results summarised as follows.
\end{enumerate}
$$\Sigma w = 1145.3 , \quad \Sigma w ^ { 2 } = 88042.14$$
(a) Calculate the mean and variance of the weight of the players.
Due to injury, one of the players who weighed 79.2 kg was replaced with another player who weighed 63.5 kg .\\
(b) Without further calculation state the effect of this change on the mean and variance of the weight of the players in the team. Explain your answers.\\
(4 marks)\\
\hfill \mbox{\textit{Edexcel S1 Q1 [9]}}