| Exam Board | OCR |
|---|---|
| Module | PURE |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Topic | Data representation |
| Type | State advantages of diagram types |
| Difficulty | Easy -1.8 This is a straightforward data representation question requiring basic arithmetic to complete a two-way table, simple probability calculations (dividing frequencies), and understanding of random sampling methodology. All parts involve routine recall and application of standard techniques with no problem-solving insight required. |
| Spec | 2.01a Population and sample: terminology2.03c Conditional probability: using diagrams/tables |
| \multirow{2}{*}{} | Town | |||
| A | B | C | Total | |
| adult | ||||
| child | ||||
| Total | ||||
| Answer | Marks | Guidance |
|---|---|---|
| \((55)\ 115\ (60)\) and \((230)\) / \((65)\ (35)\ 70\) and \(170\) / \(120\ (150)\ 130\) and \((400)\) | B1, B1, [1] | B1 for 10 correct numbers |
| Answer | Marks | Guidance |
|---|---|---|
| \(\frac{55}{400}\) ISW or \(\frac{11}{80}\) or \(0.1375\) or \(0.138\) (3 sf) | B1, [1] | NB If figures for A in the table are correct, but those for B and C are wrong, correct answers to parts (b)(i), (ii) can be obtained correctly. |
| Answer | Marks |
|---|---|
| \(\frac{55}{120}\) ISW or \(\frac{11}{24}\) or \(0.458\) (3 sf) | B1, [1] |
| Answer | Marks | Guidance |
|---|---|---|
| Kareem because, e.g. the 2nd digit of each number is the same as the 1st digit of the next | B1, [1] | oe. Allow Kareem because the numbers are not independent. |
| Answer | Marks | Guidance |
|---|---|---|
| Only 820 students or \(850 > 820\) | B1, [1] | oe |
# Question 10:
## Part (a):
$(55)\ 115\ (60)$ and $(230)$ / $(65)\ (35)\ 70$ and $170$ / $120\ (150)\ 130$ and $(400)$ | B1, B1, [1] | B1 for 10 correct numbers
## Part (b)(i):
$\frac{55}{400}$ ISW or $\frac{11}{80}$ or $0.1375$ or $0.138$ (3 sf) | B1, [1] | NB If figures for A in the table are correct, but those for B and C are wrong, correct answers to parts (b)(i), (ii) can be obtained correctly.
## Part (b)(ii):
$\frac{55}{120}$ ISW or $\frac{11}{24}$ or $0.458$ (3 sf) | B1, [1] |
## Part (c)(i):
Kareem because, e.g. the 2nd digit of each number is the same as the 1st digit of the next | B1, [1] | oe. Allow Kareem because the numbers are not independent.
## Part (c)(ii):
Only 820 students or $850 > 820$ | B1, [1] | oe
---10 Jane conducted a survey. She chose a sample of people from three towns, A, B and C. She noted the following information.
400 people were chosen.\\
230 people were adults.\\
55 adults were from town A .\\
65 children were from town A .\\
35 children were from town B .\\
150 people were from town B .
\begin{enumerate}[label=(\alph*)]
\item In the Printed Answer Booklet, complete the two-way frequency table.
\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
\multirow{2}{*}{} & \multicolumn{3}{|c|}{Town} & \\
\hline
& A & B & C & Total \\
\hline
adult & & & & \\
\hline
child & & & & \\
\hline
Total & & & & \\
\hline
\end{tabular}
\end{center}
\item One of the people is chosen at random.
\begin{enumerate}[label=(\roman*)]
\item Find the probability that this person is an adult from town A .
\item Given that the person is from town A , find the probability that the person is an adult.
For another survey, Jane wanted to choose a random sample from the 820 students living in a particular hostel. She numbered the students from 1 to 820 and then generated some random numbers on her calculator.
The random numbers were 0.114287562 and 0.081859817 .
Jane's friend Kareem used these figures to write down the following sample of five student numbers.
114, 142, 428, 287 and 756
Jane used the same figures to write down the following sample of five student numbers.\\
114, 287, 562, 81 and 817
\end{enumerate}\item \begin{enumerate}[label=(\roman*)]
\item State, with a reason, which one of these samples is not random.
\item Explain why Jane omitted the number 859 from her sample.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR PURE Q10 [6]}}