| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 9 |
| 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 application of coding formulas for mean and standard deviation with grouped data. Part (a) requires direct substitution into standard formulas (reverse the coding transformation), part (b) tests understanding of why grouped data gives estimates (a bookwork explanation), and part (c) requires comparing mean to median for skewness. All steps are routine S1 techniques with no problem-solving or novel insight required. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation5.02c Linear coding: effects on mean and variance |
| Answer | Marks | Guidance |
|---|---|---|
| \(\bar{y} = \frac{37}{80} = 0.4625\) | M1 | |
| \(\bar{C} = (250 \times 0.4625) + 3250 = £3366\) (nearest £) | M1 A1 | |
| std. dev. of \(y = \sqrt{\frac{2317}{80} - 0.4625^2} = 5.3618\) | M1 | |
| std. dev. of \(C = 250 \times 5.3618 = £1340\) (nearest £) | M1 A1 | |
| used midpoints to represent data in each group | B1 | |
| median < mean \(\therefore\) +vely skewed | B1 | |
| e.g. most cost a similar amount but some people spend a lot more | B1 | (9) |
| $\bar{y} = \frac{37}{80} = 0.4625$ | M1 | |
| $\bar{C} = (250 \times 0.4625) + 3250 = £3366$ (nearest £) | M1 A1 | |
| std. dev. of $y = \sqrt{\frac{2317}{80} - 0.4625^2} = 5.3618$ | M1 | |
| std. dev. of $C = 250 \times 5.3618 = £1340$ (nearest £) | M1 A1 | |
| used midpoints to represent data in each group | B1 | |
| median < mean $\therefore$ +vely skewed | B1 | |
| e.g. most cost a similar amount but some people spend a lot more | B1 | (9) |3. A magazine collected data on the total cost of the reception at each of a random sample of 80 weddings.
The data is grouped and coded using $y = \frac { C - 3250 } { 250 }$, where $C$ is the mid-point in pounds of each class, giving $\sum f y = 37$ and $\sum f y ^ { 2 } = 2317$.
\begin{enumerate}[label=(\alph*)]
\item Using these values, calculate estimates of the mean and standard deviation of the cost of the receptions in the sample.
\item Explain why your answers to part (a) are only estimates.
The median of the data was $\pounds 3050$.
\item Comment on the skewness of the data and suggest a reason for it.
\end{enumerate}
\hfill \mbox{\textit{Edexcel S1 Q3 [9]}}