Statistics · Guided Practice
Data Sets
10 questions with answers and video solutions. Try each one before revealing the answer.
Midday temperatures in °C were recorded in Glasgow over the period from 1st to 9th March, inclusive:
6 8 11 12 8 5 9 7 6
Calculate the standard deviation of these temperatures, correct to 2 significant figures.
Midday temperatures in °C were recorded in Edinburgh over the period from 1st to 9th March, inclusive:
7 6 10 10 9 6 8 7 7
Calculate the standard deviation of these temperatures, correct to 2 significant figures.
Using the answers to the previous examples, make two valid comments comparing the temperatures at midday in Glasgow and Edinburgh over the period from 1st to 9th March, inclusive.
Answer
The standard deviation of 1, 2, 2, 2, 8 is equal to Find the value of a.
A company operates a bus route from the city centre to the airport. The number of passengers on six of its buses on a Monday was
32 27 34 29 31 33
(a) Calculate the mean and standard deviation of the number of passengers.
(b) The mean number of passengers the following Saturday was 28 and the standard deviation was 3.2. Make two valid comments comparing the number of passengers on each bus on Monday and Saturday.
Answer
(b) On average, the Monday buses had more passengers, as The number of passengers on each bus varied more on Saturday, as
A magazine company conducted a survey of the ages of its readers. A sample of ten readers' ages, in years, are shown below.
33 55 38 47 36 41 42 41 35 31
(a) Calculate the median and interquartile range of the ages of readers for this sample.
A newspaper company also conducted a survey of the ages of its readers. The median age of a sample of its readers was 41 years and the interquartile range was 9 years.
(b) Make two valid comments comparing the ages of the readers of the magazine and the ages of the readers of the newspaper.
Answer
(b) On average, the readers of the newspaper are older, as . The ages of the newspaper readers are more varied, as .
The prices, in pounds (£), of the cameras on display in a shop are listed below.
155 160 190 210 230 240
(a) Calculate the median and the interquartile range of these prices.
On a website, a sample of camera prices have a median of £195 and an interquartile range of £73.
(b) Make two valid comments comparing the prices of the cameras in the shop and on the website.
Answer
(b) On average, cameras on the website are cheaper (£195 < £200). The prices on the website are more varied (£73 > £70).
Ten pupils record the length of time, in minutes, it takes them to walk to school one morning.
3 11 13 15 15 16 17 18 19 22
Calculate the interquartile range of these times.
The weights, in kilograms, of a sample of rugby players in Scotland are shown.
93 103 99 105 88 106 92
(a) Calculate the mean and standard deviation of these weights.
A sample of rugby players in France has a mean weight of 105 kilograms and a standard deviation of 5.9 kilograms.
(b) Make two valid comments comparing the weights of the rugby players in the samples from Scotland and France.
Answer
A restaurant recorded the waiting times to be seated from a sample of its customers.
The waiting times, in minutes, of ten customers were:
2 20 5 14 2 4 8 18 6 15
(a) Calculate the median and interquartile range of the waiting times.
A café also recorded the waiting times to be seated from a sample of its customers.
The median waiting time at the café was 5 minutes and the interquartile range was 12 minutes.
(b) Make two valid comments comparing the waiting times at the restaurant and at the café.
Answer
(b) On average, the waiting times at the restaurant were longer than at the café, as
The waiting times at the restaurant were more consistent than at the café, as
Practice questions courtesy of Maths.scot. Full written solutions are on his site — the links above go straight to them.