| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2014 |
| Session | June |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Draw cumulative frequency graph from frequency table (equal class widths) |
| Difficulty | Easy -1.3 This is a routine S1 question requiring standard procedures: calculating cumulative frequencies from a grouped frequency table, plotting points, and reading off median and IQR from the graph. It involves no problem-solving or conceptual challenges—just mechanical application of well-practiced techniques with straightforward data. |
| Spec | 2.02a Interpret single variable data: tables and diagrams2.02f Measures of average and spread |
| Age (\(x\)) | \(20 \leqslant x < 30\) | \(30 \leqslant x < 40\) | \(40 \leqslant x < 50\) | \(50 \leqslant x < 60\) | \(60 \leqslant x < 70\) | \(70 \leqslant x < 80\) | \(80 \leqslant x < 90\) |
| Frequency | 10 | 30 | 42 | 23 | 9 | 5 | 1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Upper Bound: 20, 30, 40, 50, 60, 70, 80, 90<br>Cumulative Freq: 0, 10, 40, 82, 105, 114, 119, 120 | B1 | Cumulative frequencies all correct |
| Ogive plotted with points at correct UCB positions | G1 | Plotted within \(\frac{1}{2}\) small square. If cf not given then allow G1 for good attempt at cf; e.g. if they have 0,10,40,72,95,104,109,110 |
| G1 | For joining points (within \(\frac{1}{2}\) a square) | |
| G1 | For scales | |
| G1 | For labels | |
| All marks dep on good attempt at cumulative frequency, but not cumulative fx's or other spurious values. | ||
| Total | [5] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Median = 45 | B1 | Allow answers between 44 and 46 without checking curve. Otherwise check curve. No marks if not using diagram. Based on 60th value ft their curve (not LCB's) Allow 40 for m.p. plot without checking graph |
| \(Q1 = 37\), \(Q3 = 53\) | B1 | For Q3 or Q1 Allow Q1 between 37 and 38 without checking. Allow Q3 between 52 and 54 without checking. Based on 30th and 90th values ft their curve (not LCB's) Allow Q1 = 32; Q3 = 48 without checking graph |
| Inter-quartile range = \(53 - 37 = 16\) | B1 | For IQR providing both Q1 and Q3 are correct. Allow from mid-point plot. Must be good attempt at cumulative frequency in part (i) to score any marks here. Lines of best fit: B0 B0 B0 here. Also cumulative frequency bars: B0 B0 B0 here |
| Total | [3] |
## (i)
| **Answer** | **Marks** | **Guidance** |
|---|---|---|
| Upper Bound: 20, 30, 40, 50, 60, 70, 80, 90<br>Cumulative Freq: 0, 10, 40, 82, 105, 114, 119, 120 | B1 | Cumulative frequencies all correct |
| Ogive plotted with points at correct UCB positions | G1 | Plotted within $\frac{1}{2}$ small square. If cf not given then allow G1 for good attempt at cf; e.g. if they have 0,10,40,72,95,104,109,110 |
| | G1 | For joining points (within $\frac{1}{2}$ a square) |
| | G1 | For scales |
| | G1 | For labels |
| | | All marks dep on good attempt at cumulative frequency, but not cumulative fx's or other spurious values. |
| **Total** | **[5]** | |
## (ii)
| **Answer** | **Marks** | **Guidance** |
|---|---|---|
| Median = 45 | B1 | Allow answers between 44 and 46 without checking curve. Otherwise check curve. No marks if not using diagram. Based on 60th value ft their curve (not LCB's) Allow 40 for m.p. plot without checking graph |
| $Q1 = 37$, $Q3 = 53$ | B1 | For Q3 or Q1 Allow Q1 between 37 and 38 without checking. Allow Q3 between 52 and 54 without checking. Based on 30th and 90th values ft their curve (not LCB's) Allow Q1 = 32; Q3 = 48 without checking graph |
| Inter-quartile range = $53 - 37 = 16$ | B1 | For IQR providing both Q1 and Q3 are correct. Allow from mid-point plot. Must be good attempt at cumulative frequency in part (i) to score any marks here. Lines of best fit: B0 B0 B0 here. Also cumulative frequency bars: B0 B0 B0 here |
| **Total** | **[3]** | |
---The ages, $x$ years, of the senior members of a running club are summarised in the table below.
\begin{tabular}{|c|c|c|c|c|c|c|c|}
\hline
Age ($x$) & $20 \leqslant x < 30$ & $30 \leqslant x < 40$ & $40 \leqslant x < 50$ & $50 \leqslant x < 60$ & $60 \leqslant x < 70$ & $70 \leqslant x < 80$ & $80 \leqslant x < 90$ \\
\hline
Frequency & 10 & 30 & 42 & 23 & 9 & 5 & 1 \\
\hline
\end{tabular}
\begin{enumerate}[label=(\roman*)]
\item Draw a cumulative frequency diagram to illustrate the data. [5]
\item Use your diagram to estimate the median and interquartile range of the data. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR MEI S1 2014 Q1 [8]}}