| Exam Board | OCR |
|---|---|
| Module | S1 (Statistics 1) |
| Year | 2007 |
| Session | June |
| Marks | 10 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Data representation |
| Type | Compare or interpret cumulative frequency graphs |
| Difficulty | Moderate -0.8 This question requires reading values from cumulative frequency curves and interpreting them, which are standard S1 skills. Part (i) involves comparing final cumulative frequencies, part (ii)(a) requires reading median, quartiles, and specific proportions from the graph, and part (ii)(b) asks for straightforward interpretation. All techniques are routine for this topic with no novel problem-solving required. |
| Spec | 2.02f Measures of average and spread |
| Year |
|
|
|
| ||||||||
| 1991 | 27.5 | 7.3 | \(33 \%\) | \(9 \%\) | ||||||||
| 2001 | \(18 \%\) |
| Answer | Marks | Guidance |
|---|---|---|
| 100 000 to 110 000 | B1 ind | Or fewer in 2001 |
| B1 ind | Allow digits100 to 110 | |
| 2 |
| Answer | Marks |
|---|---|
| Median = 29 to 29.9 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 23 to 26.3% | M1 | Or one correct quartile and subtr |
| A1 | NOT from incorrect wking | |
| M1 | ×1000, but allow without | |
| A1 | Rnded to 1 dp or integer 73.7 to 77%; SC1 | |
| 5 |
| Answer | Marks | Guidance |
|---|---|---|
| % younger mothers less oe | B1 | Or 1991 younger |
| Any two | ||
| B1 | Or 1991 steeper so more younger; B2 | |
| B1 | 3 NOT mean gter | |
| Ignore extra |
### Part i
1991
100 000 to 110 000 | B1 ind | Or fewer in 2001
| B1 ind | Allow digits100 to 110
| 2 |
### Part iia
Median = 29 to 29.9 | B1 |
Quartiles 33 to 34, 24.5 to 26
$= 7.5$ to 9.5
140 to 155
23 to 26.3% | M1 | Or one correct quartile and subtr
| A1 | NOT from incorrect wking
| M1 | ×1000, but allow without
| A1 | Rnded to 1 dp or integer 73.7 to 77%; SC1
| | 5 |
### Part b
Older
Median (or ave) greater
% older mothers greater oe
% younger mothers less oe | B1 | Or 1991 younger
| | Any two
| B1 | Or 1991 steeper so more younger; B2
| B1 | 3 NOT mean gter
| | Ignore extra
**Total: 10**
---5 The numbers of births, in thousands, to mothers of different ages in England and Wales, in 1991 and 2001 are illustrated by the cumulative frequency curves.
Cumulative frequency (000's)\\
\includegraphics[max width=\textwidth, alt={}, center]{dfad6626-75ca-4dbd-9c45-42f809c163f3-3_949_1338_461_479}\\
(i) In which of these two years were there more births? How many more births were there in this year?\\
(ii) The following quantities were estimated from the diagram.
\begin{center}
\begin{tabular}{ | c | c | c | c | c | }
\hline
Year & \begin{tabular}{ c }
M edian age \\
(years) \\
\end{tabular} & \begin{tabular}{ c }
Interquartile \\
range (years) \\
\end{tabular} & \begin{tabular}{ c }
Proportion of mothers \\
giving birth aged below 25 \\
\end{tabular} & \begin{tabular}{ c }
Proportion of mothers \\
giving birth aged 35 or above \\
\end{tabular} \\
\hline
1991 & 27.5 & 7.3 & $33 \%$ & $9 \%$ \\
\hline
2001 & & & & $18 \%$ \\
\hline
\end{tabular}
\end{center}
\begin{enumerate}[label=(\alph*)]
\item Find the values missing from the table.
\item Did the women who gave birth in 2001 tend to be younger or older or about the same age as the women who gave birth in 1991? Using the table and your values from part (a), give two reasons for your answer.
\end{enumerate}
\hfill \mbox{\textit{OCR S1 2007 Q5 [10]}}