Measures of dispersionEdexcel International A Level Maths: Flashcards

What these 13 flashcards ask

Definition of the range?
Formula for the interquartile range?
Positions of Q1, Q2 and Q3 in n ordered values?
What does the IQR measure?
What is a 10th to 90th interpercentile range?
Formula for the variance?
Formula for the variance from a frequency table?
How do you get the standard deviation from the variance?
Units of variance compared with the data?
If y=ax+b, what is the standard deviation of y?
What does a smaller standard deviation tell you?
Which spread measure should accompany the median?
What is the effect of adding a value equal to the mean?

Exam questions on Measures of dispersion

The reaction times, in tenths of a second, of eight athletes were 2, 4, 4, 4, 5, 5, 7 and 9.
Find the interquartile range of the eight values.2 marks
A sample of 20 delivery times, $x$ minutes, has $\sum x=140$ and $\sum x^2=1160$ . A second sample of delivery times, from another firm, has the same mean but a standard deviation of 5 minutes.
A 21st delivery time of 7 minutes is added to the first sample. Find the new standard deviation.2 marks
The waiting times, in minutes, of 80 patients at a clinic are summarised as follows: under 10 minutes, 6 patients; 10 to under 20 minutes, 24 patients; 20 to under 30 minutes, 28 patients; 30 to under 40 minutes, 16 patients; 40 to under 60 minutes, 6 patients. Assume that times are spread evenly within each class.
Estimate the interquartile range of the waiting times.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).