OCR S1 (Statistics 1) 2010 June

1 The marks of some students in a French examination were summarised in a grouped frequency distribution and a cumulative frequency diagram was drawn, as shown below.
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1. Estimate how many students took the examination.
2. How can you tell that no student scored more than 55 marks?
3. Find the greatest possible range of the marks.
4. The minimum mark for Grade C was 27 . The number of students who gained exactly Grade C was the same as the number of students who gained a grade lower than C. Estimate the maximum mark for Grade C.
5. In a German examination the marks of the same students had an interquartile range of 16 marks. What does this result indicate about the performance of the students in the German examination as compared with the French examination?

2 Three skaters, \(A , B\) and \(C\), are placed in rank order by four judges. Judge \(P\) ranks skater \(A\) in 1st place, skater \(B\) in 2nd place and skater \(C\) in 3rd place.

1. Without carrying out any calculation, state the value of Spearman's rank correlation coefficient for the following ranks. Give a reason for your answer. \href{http://physicsandmathstutor.com}{physicsandmathstutor.com}

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7 The menu below shows all the dishes available at a certain restaurant. A group of friends decide that they will share a total of 2 different rice dishes, 3 different main dishes and 4 different vegetable dishes from this menu. Given these restrictions,

1. find the number of possible combinations of dishes that they can choose to share,
2. assuming that all choices are equally likely, find the probability that they choose boiled rice. The friends decide to add a further restriction as follows. If they choose boiled rice, they will not choose potatoes.
3. Find the number of possible combinations of dishes that they can now choose.

8 The proportion of people who watch West Street on television is \(30 \%\). A market researcher interviews people at random in order to contact viewers of West Street. Each day she has to contact a certain number of viewers of West Street.

1. Near the end of one day she finds that she needs to contact just one more viewer of West Street. Find the probability that the number of further interviews required is
   (a) 4 ,

10 8

(a) 8

(b) \section*{PLEASE DO NOT WRITE ON THIS PAGE} RECOGNISING ACHIEVEMENT