| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Calculate statistics from discrete frequency table |
| Difficulty | Easy -1.2 This is a straightforward S1 question requiring standard application of formulas for mean and standard deviation from a frequency table, followed by routine linear transformation of statistics. The calculations are mechanical with no conceptual challenges or problem-solving required beyond recalling the formulas Σfx/Σf and understanding that multiplying data by a constant multiplies both mean and SD by that constant. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation5.02c Linear coding: effects on mean and variance |
| Number of loaves | 0 | 1 | 2 | 3 | 4 | 5 |
| Frequency | 37 | 23 | 11 | 3 | 0 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| \(\text{Mean} = \frac{0\times37+1\times23+2\times11+3\times3+4\times0+5\times1}{75} = \frac{59}{75} = 0.787\) | M1, A1 | |
| \(S_{xx} = 0^2\times37+1^2\times23+2^2\times11+3^2\times3+4^2\times0+5^2\times1 - \frac{59^2}{75} = 72.59\) | M1, M1dep | M1 for \(\Sigma fx^2\) s.o.i.; M1 dep for good attempt at \(S_{xx}\); NOTE M1M0 if their \(S_{xx}<0\) |
| \(s = \sqrt{\frac{72.59}{74}} = 0.99\) | A1 CAO |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| New mean \(= 0.787 \times £1.04 = £0.818\) or 81.8 pence | B1 | ft their mean |
| New \(s = 0.99 \times £1.04 = £1.03\) or 103 pence | B1 | ft their \(s\) |
| B1 | For correct units *dep* on at least 1 correct (ft) |
## Question 6:
### Part (i)
| Answer/Working | Marks | Guidance |
|---|---|---|
| $\text{Mean} = \frac{0\times37+1\times23+2\times11+3\times3+4\times0+5\times1}{75} = \frac{59}{75} = 0.787$ | M1, A1 | |
| $S_{xx} = 0^2\times37+1^2\times23+2^2\times11+3^2\times3+4^2\times0+5^2\times1 - \frac{59^2}{75} = 72.59$ | M1, M1dep | M1 for $\Sigma fx^2$ s.o.i.; M1 dep for good attempt at $S_{xx}$; NOTE M1M0 if their $S_{xx}<0$ |
| $s = \sqrt{\frac{72.59}{74}} = 0.99$ | A1 CAO | |
### Part (ii)
| Answer/Working | Marks | Guidance |
|---|---|---|
| New mean $= 0.787 \times £1.04 = £0.818$ or 81.8 pence | B1 | ft their mean |
| New $s = 0.99 \times £1.04 = £1.03$ or 103 pence | B1 | ft their $s$ |
| | B1 | For correct units *dep* on at least 1 correct (ft) |6 A retail analyst records the numbers of loaves of bread of a particular type bought by a sample of shoppers in a supermarket.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | }
\hline
Number of loaves & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline
Frequency & 37 & 23 & 11 & 3 & 0 & 1 \\
\hline
\end{tabular}
\end{center}
(i) Calculate the mean and standard deviation of the numbers of loaves bought per person.\\
(ii) Each loaf costs $\pounds 1.04$. Calculate the mean and standard deviation of the amount spent on loaves per person.
\hfill \mbox{\textit{OCR MEI S1 Q6 [8]}}