| Exam Board | OCR MEI |
|---|---|
| Module | S1 (Statistics 1) |
| 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 -1.8 This is a routine S1 statistics question requiring straightforward application of standard procedures: calculating cumulative frequencies from a frequency table, plotting points, and reading off median/IQR. It involves no problem-solving, conceptual depth, or novel insight—purely mechanical execution of textbook methods. |
| 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 |
| Cumulative frequencies: Upper Bound: 20, 30, 40, 50, 60, 70, 80, 90; Cumulative Freq: 0, 10, 40, 82, 105, 114, 119, 120 | B1 | All correct |
| Plotted 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 |
| Joining points (within \(\frac{1}{2}\) a square) | G1 | |
| Scales | G1 | |
| Labels | G1 | All marks dep on good attempt at cumulative frequency, but not cumulative \(fx\)'s or other spurious values |
| 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 \(60^{\text{th}}\) value, ft their curve (not LCB's). Allow 40 for m.p. plot without checking graph. B0 for interpolation. If max value wrong (e.g. 110) FT their max value for all 3 marks |
| \(Q_1 = 37\), \(Q_3 = 53\) | B1 | For \(Q_3\) or \(Q_1\): allow \(Q_1\) between 37 and 38 without checking; allow \(Q_3\) between 52 and 54 without checking. Based on \(30^{\text{th}}\) and \(90^{\text{th}}\) values, ft their curve (not LCB's). Allow \(Q_1 = 32\); \(Q_3 = 48\) without checking graph. B0 for interpolation. B2 for correct IQR from graph if quartiles not stated but indicated on graph |
| Inter-quartile range \(= 53 - 37 = 16\) | B1 | For IQR providing both \(Q_1\) and \(Q_3\) 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 |
## Question 3:
### Part (i)
| Answer | Marks | Guidance |
|--------|-------|----------|
| Cumulative frequencies: Upper Bound: 20, 30, 40, 50, 60, 70, 80, 90; Cumulative Freq: 0, 10, 40, 82, 105, 114, 119, 120 | B1 | All correct |
| Plotted 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 |
| Joining points (within $\frac{1}{2}$ a square) | G1 | |
| Scales | G1 | |
| Labels | G1 | All marks dep on good attempt at cumulative frequency, but not cumulative $fx$'s or other spurious values |
### Part (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 $60^{\text{th}}$ value, ft their curve (not LCB's). Allow 40 for m.p. plot without checking graph. B0 for interpolation. If max value wrong (e.g. 110) FT their max value for all 3 marks |
| $Q_1 = 37$, $Q_3 = 53$ | B1 | For $Q_3$ or $Q_1$: allow $Q_1$ between 37 and 38 without checking; allow $Q_3$ between 52 and 54 without checking. Based on $30^{\text{th}}$ and $90^{\text{th}}$ values, ft their curve (not LCB's). Allow $Q_1 = 32$; $Q_3 = 48$ without checking graph. B0 for interpolation. B2 for correct IQR from graph if quartiles not stated but indicated on graph |
| Inter-quartile range $= 53 - 37 = 16$ | B1 | For IQR providing both $Q_1$ and $Q_3$ 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 |
---3 The ages, $x$ years, of the senior members of a running club are summarised in the table below.
\begin{center}
\begin{tabular}{ | l | 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}
\end{center}
(i) Draw a cumulative frequency diagram to illustrate the data.\\
(ii) Use your diagram to estimate the median and interquartile range of the data.
\hfill \mbox{\textit{OCR MEI S1 Q3 [8]}}