Compare using calculated statistics - Measures of Location and Spread

CAIE S1 2004 June Q1

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.

OCR MEI AS Paper 2 2018 June Q7

7 Rose and Emma each wear a device that records the number of steps they take in a day. All the results for a 7-day period are given in Fig. 7. \begin{table}[h]

Day	1	2	3	4	5	6	7
Rose	10014	11262	10149	9361	9708	9921	10369
Emma	9204	9913	8741	10015	10261	7391	10856

\captionsetup{labelformat=empty} \caption{Fig. 7}

\end{table} The 7-day mean is the mean number of steps taken in the last 7 days. The 7-day mean for Rose is 10112 .

Calculate the 7-day mean for Emma. At the end of day 8 a new 7-day mean is calculated by including the number of steps taken on day 8 and omitting the number of steps taken on day 1 . On day 8 Rose takes 10259 steps.
Determine the number of steps Emma must take on day 8 so that her 7 -day mean at the end of day 8 is the same as for Rose. In fact, over a long period of time, the mean of the number of steps per day that Emma takes is 10341 and the standard deviation is 948.
Determine whether the number of steps Emma needs to take on day 8 so that her 7 -day mean is the same as that for Rose in part (ii) is unusually high.

AQA AS Paper 2 2022 June Q13

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
1. Show how Siti's claim of 'over 75\%' has been obtained.
  13
(ii) Using your knowledge of the Large Data Set, make two comments on the validity of Siti's claim. Comment 1
\section*{Comment 2}