Measures of central tendency and spreadAQA A-Level Maths: Flashcards

What these 13 flashcards ask

Formula for the mean?
Which average is not affected by extreme values?
Formula for variance using summary statistics?
Standard deviation in terms of variance?
What does a larger standard deviation mean?
What is the interquartile range?
Which measures of spread are not affected by extremes?
How do you find the median from a frequency table?
What two comments compare two data sets?
A value equal to the mean is added. What happens to the mean and standard deviation?
How do you correct \sum x for a wrong value?
How do you find the standard deviation of two combined sets?
What are the units of the standard deviation?

Exam questions on Measures of central tendency and spread

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
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
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

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).