| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Measures of Location and Spread |
| Type | Vertical line chart construction |
| Difficulty | Easy -1.8 This is a straightforward data handling question requiring basic chart construction and standard calculations of mean and RMSD from a frequency table. Part (iii) involves a simple linear transformation (present = 30 - absent). All techniques are routine recall with no problem-solving or conceptual challenge beyond AS-level statistics basics. |
| Spec | 2.02f Measures of average and spread2.02g Calculate mean and standard deviation |
| Number of absentees | 0 | 1 | 2 | 3 | 4 | 5 | 6 | \(> 6\) |
| Frequency | 8 | 15 | 11 | 8 | 3 | 4 | 1 | 0 |
| Answer | Marks |
|---|---|
| G1 | labelled linear scales on both axes |
| G1 | heights |
| Answer | Marks |
|---|---|
| B1 | for mean |
| M1 | for attempt at \(S_{xx}\) |
| A1 | CAO |
| Answer | Marks |
|---|---|
| B1 | FT their mean |
| B1 | FT their rmsd |
# Question 4:
## Part (i)
Bar chart with correct heights
| G1 | labelled linear scales on both axes |
| G1 | heights |
**Total: 2 marks**
## Part (ii)
$\text{Mean} = \dfrac{99}{50} = 1.98$
$S_{xx} = 315 - \dfrac{99^2}{50} \quad (= 118.98)$
$\text{rmsd} = \sqrt{\dfrac{118.98}{50}} = 1.54$
| B1 | for mean |
| M1 | for attempt at $S_{xx}$ |
| A1 | CAO |
*NB full marks for correct results from recommended method which is use of calculator functions*
**Total: 3 marks**
## Part (iii)
New mean $= 30 - 1.98 = 28.02$
New rmsd $= 1.54$ (unchanged)
| B1 | FT their mean |
| B1 | FT their rmsd |
**Total: 2 marks**
---4 The numbers of absentees per day from Mrs Smith's reception class over a period of 50 days are summarised below.
\begin{center}
\begin{tabular}{ | l | c | c | c | c | c | c | c | c | }
\hline
Number of absentees & 0 & 1 & 2 & 3 & 4 & 5 & 6 & $> 6$ \\
\hline
Frequency & 8 & 15 & 11 & 8 & 3 & 4 & 1 & 0 \\
\hline
\end{tabular}
\end{center}
(i) Illustrate these data by means of a vertical line chart.\\
(ii) Calculate the mean and root mean square deviation of these data.\\
(iii) There are 30 children in Mrs Smith's class altogether. Find the mean and root mean square deviation of the number of children who are present during the 50 days.
\hfill \mbox{\textit{OCR MEI S1 Q4 [7]}}