| Exam Board | Edexcel |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2011 |
| Session | January |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Adding data values |
| Difficulty | Easy -1.8 This is a straightforward question requiring only basic arithmetic to find a mean from given data, then qualitative reasoning about how swapping digits affects the mean. No problem-solving or conceptual depth required—purely mechanical calculation and simple observation that the corrections cancel out. |
| Spec | 2.02f Measures of average and spread |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(2.8 + 5.6 + 2.3 + 9.4 + 0.5 + 1.8 + 84.6 = 107\) | M1 | For a clear attempt to add the two sums; accept full expression or \(2.8 + 5.6 + \ldots + 84.6 = x\) where \(100 < x < 110\) |
| mean \(= 107/28 = 3.821\ldots\) awrt 3.8 | A1 | Accept \(\frac{107}{28}\) or \(3\frac{23}{28}\); correct answer implies M1A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| It will have no effect | B1 | For clearly stating it will have no effect ("roughly the same" is B0) |
| since one is 4.5 under what it should be and the other is 4.5 above | dB1 | Supporting reason mentioning increase and decrease are the same with numerical value(s); e.g. sum is still 107, or \(9.4 - 4.9 = 5 - 0.5\); dependent on first B1 so B0B1 is not possible |
# Question 2:
## Part (a)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $2.8 + 5.6 + 2.3 + 9.4 + 0.5 + 1.8 + 84.6 = 107$ | M1 | For a clear attempt to add the two sums; accept full expression or $2.8 + 5.6 + \ldots + 84.6 = x$ where $100 < x < 110$ |
| mean $= 107/28 = 3.821\ldots$ awrt **3.8** | A1 | Accept $\frac{107}{28}$ or $3\frac{23}{28}$; correct answer implies M1A1 |
## Part (b)
| Answer/Working | Marks | Guidance |
|---|---|---|
| It will have no effect | B1 | For clearly stating it will have no effect ("roughly the same" is B0) |
| since one is 4.5 under what it should be and the other is 4.5 above | dB1 | Supporting reason mentioning increase and decrease are the same with numerical value(s); e.g. sum is still 107, or $9.4 - 4.9 = 5 - 0.5$; dependent on first B1 so B0B1 is not possible |
---\begin{enumerate}
\item Keith records the amount of rainfall, in mm , at his school, each day for a week. The results are given below.\\
0.0\\
0.5\\
1.8\\
2.8\\
2.3\\
5.6\\
9.4
\end{enumerate}
Jenny then records the amount of rainfall, $x \mathrm {~mm}$, at the school each day for the following 21 days. The results for the 21 days are summarised below.
$$\sum x = 84.6$$
(a) Calculate the mean amount of rainfall during the whole 28 days.
Keith realises that he has transposed two of his figures. The number 9.4 should have been 4.9 and the number 0.5 should have been 5.0
Keith corrects these figures.\\
(b) State, giving your reason, the effect this will have on the mean.\\
\hfill \mbox{\textit{Edexcel S1 2011 Q2 [4]}}