Measures of central tendency and spreadAQA A-Level Maths: Mind map

Exam questions on Measures of central tendency and spread

1. Six students' times, in minutes, to complete a puzzle are 12, 15, 15, 18, 22 and 26. In this question the standard deviation uses divisor $n$.
   A seventh student takes exactly 18 minutes. State, with a reason, the effect of including this time on (i) the mean and (ii) the standard deviation.2 marks
2. A courier firm records 25 delivery times, $x$ minutes. The summary statistics are $\sum x=400$ and $\sum x^2=7000$. The standard deviation uses divisor $n$.
   One recorded time of 40 minutes was a mistake: it should have been 20 minutes. Find the correct mean.2 marks
3. A factory has two machines, A and B, that fill bags of sugar labelled 1000 g. For a sample of bags from machine A the mean mass is 1004 g and the standard deviation is 3.2 g. For a sample from machine B the mean is 1001 g and the standard deviation is 1.1 g.
   Compare the two machines and state which you would recommend, giving reasons.3 marks