June 2023 Paper 3 Q15

AQACurrent spec11 marksIncludes samplingData ProcessingDRVsLarge Data Set

15

(a) A random sample of eight cars was selected from the Large Data Set.

The masses of these cars, in kilograms, were as follows.

950989124714151506168018332040

It is given that, for the population of cars in the Large Data Set:

\[\begin{aligned}\text{lower quartile} &= 1167 \\ \text{median} &= 1393 \\ \text{upper quartile} &= 1570\end{aligned}\]
(i) It was decided to remove any of the masses which fall outside the following interval.\[\text{median} - 1.5 \times \text{interquartile range} \leqslant \text{mass} \leqslant \text{median} + 1.5 \times \text{interquartile range}\]

Show that only one of the eight masses in the sample should be removed. [3 marks]

(ii) Write down the statistical name for the mass that should be removed in part (a)(i). [1 mark]
(b) The table shows the probability distribution of the number of previous owners, \(N\), for a sample of cars taken from the Large Data Set.
\(n\)0123456 or more
\(\mathrm{P}(N = n)\)0.140.37\(0.9k\)0.25\(0.4k\)\(1.7k\)0

Find the value of \(\mathrm{P}(1 \leqslant N \lt 5)\) [4 marks]

(c) An expert team is investigating whether there have been any changes in CO2 emissions from all cars taken from the Large Data Set.

The team decided to collect a quota sample of 200 cars to reflect the different years and the different makes of cars in the Large Data Set.

(i) Using your knowledge of the Large Data Set, explain how the team can collect this sample. [2 marks]
(ii) Describe one disadvantage of quota sampling. [1 mark]
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