Compare using calculated statistics

Questions that provide raw data or summary statistics (mean, standard deviation, median, IQR) and ask students to calculate and compare measures of location and spread between two datasets.

3 questions · Moderate -0.9

2.02f Measures of average and spread

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CAIE S1 2004 June Q1

4 marks Easy -1.2

1 Two cricket teams kept records of the number of runs scored by their teams in 8 matches. The scores are shown in the following table.

Team \(A\)	150	220	77	30	298	118	160	57
Team \(B\)	166	142	170	93	111	130	148	86

Find the mean and standard deviation of the scores for team \(A\). The mean and standard deviation for team \(B\) are 130.75 and 29.63 respectively.
State with a reason which team has the more consistent scores.

AQA AS Paper 2 2022 June Q13

6 marks Moderate -0.8

13 Two random samples of 12 NOX emissions (in \(\mathrm { g } / \mathrm { km }\) ) were taken from the Large Data Set. One sample was taken from the 2002 data and the other sample from the 2016 data.
The sample data are shown below:

\multirow{2}{*}{2002}	0.031	0.019	0.091	0.025	0.030	0.061
	0.047	0.029	0.059	0.363	0.330	0.376

\multirow{2}{*}{2016}	0.005	0.047	0.053	0.063	0.026	0.013
	0.058	0.012	0.010	0.010	0.008	0.008

The mean and standard deviation of the 2002 sample data are 0.122 and 0.137 respectively. 13

Find the mean and standard deviation of the 2016 sample data giving your answers correct to three decimal places.
13
Siti claims these samples show that, on average, the NOX emissions across all makes of car in all areas of the UK have fallen by over 75\% between 2002 and 2016. 13 (b) (i) Show how Siti's claim of 'over 75\%' has been obtained.
13 (b) (ii) Using your knowledge of the Large Data Set, make two comments on the validity of Siti's claim. Comment 1
\section*{Comment 2}

OCR S1 2009 June Q6

11 marks Moderate -0.8

Last year Eleanor played 11 rounds of golf. Her scores were as follows: 79, 71, 80, 67, 67, 74, 66, 65, 71, 66, 64.

Calculate the mean of these scores and show that the standard deviation is 5.31, correct to 3 significant figures. [4]
Find the median and interquartile range of the scores. [4]

This year, Eleanor also played 11 rounds of golf. The standard deviation of her scores was 4.23, correct to 3 significant figures, and the interquartile range was the same as last year.

Give a possible reason why the standard deviation of her scores was lower than last year although her interquartile range was unchanged. [1]

In golf, smaller scores mean a better standard of play than larger scores. Ken suggests that since the standard deviation was smaller this year, Eleanor's overall standard has improved.

Explain why Ken is wrong. [1]
State what the smaller standard deviation does show about Eleanor's play. [1]