Outliers

The oxides of nitrogen emissions, F g/km, of a car registered in 2000 can be modelled by a normal distribution with mean 0.41 and standard deviation 0.07

Find P(F < 0.39)

Find P(0.3 < F < 0.5)

Find P(F > 0.6)

Explain why P(F ≥ 0.6) = P(F > 0.6) in this model.

The oxides of nitrogen emissions, F g/km, of a car in 2010 can be modelled by a normal distribution with mean 0.36 and standard deviation 0.09

Compare the oxides of nitrogen emissions in 2000 with those in 2010.

A researcher collected data on the oxides of nitrogen emissions from the Large Data Set for cars registered in 2002 and 2016.

The researcher cleaned the data by removing the details for some cars.

Using your knowledge of the Large Data Set, give one reason why the researcher cleaned the data.

The researcher wished to make a comparison between the oxides of nitrogen emissions for a sample of Nissan cars in their local town from 2016 with the data from all cars registered in the same year in the Large Data Set.

Using your knowledge of the Large Data Set, give one reason why a meaningful comparison could not be made.

A random sample of eight cars was selected from the Large Data Set.

The masses of these cars, in kilograms, were as follows.

950 989 1247 1415 1506 1680 1833 2040

It is given that, for the population of cars in the Large Data Set:

It was decided to remove any of the masses which fall outside the following interval.

median 15 interquartile range mass median 15 interquartile range

Show that only one of the eight masses in the sample should be removed.

Write down the statistical name for the mass that should be removed in part (a)(i).

The table shows the probability distribution of the number of previous owners, N, for a sample of cars taken from the Large Data Set.

	0	1	2	3	4	5	6 or more
P( = )	0.14	0.37	0.9k	0.25	0.4k	1.7k	0

An expert team is investigating whether there have been any changes in CO₂ emissions from all cars taken from the Large Data Set.

The team decided to collect a quota sample of 200 cars to reflect the different years and the different makes of cars in the Large Data Set.

Using your knowledge of the Large Data Set, explain how the team can collect this sample.

Describe one disadvantage of quota sampling.

The box plot below shows summary data for the number of minutes late that buses arrived at a rural bus stop.

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Minutes late

Identify which term best describes the distribution of this data.

Circle your answer.

negatively skewed normal positively skewed symmetrical

A reporter is writing an article on the CO₂ emissions from vehicles using the Large Data Set.

The reporter claims that the Large Data Set shows that the CO₂ emissions from all vehicles in the UK have declined every year from 2002 to 2016.

Using your knowledge of the Large Data Set, give two reasons why this claim is invalid.

The table below is an extract from the Large Data Set.

Calculate the mean and standard deviation of CO₂ emissions in the table.

Any value more than 2 standard deviations from the mean can be identified as an outlier.

Determine, using this definition of an outlier, if there are any outliers in this sample of

Fully justify your answer.

Maria claims that the last line in the table must contain two errors.

Use your knowledge of the Large Data Set to comment on Maria’s claim.

Amelia decides to analyse the heights of members of her school rowing club.

The heights of a random sample of 10 rowers are shown in the table below.

Any value more than 2 standard deviations from the mean may be regarded as an outlier.

Verify that Ann’s height is an outlier.

Fully justify your answer.

Amelia thinks she may have written down Ann’s height incorrectly.

If Ann’s height were discarded, state with a reason what, if any, difference this would make to the mean and standard deviation.

The graph below shows the amount of salt, in grams, purchased per person per week in England between 2001–02 and 2014, based upon the Large Data Set.

Meera and Gemma are arguing about what this graph shows.

Meera believes that the amount of salt consumed by people decreased greatly during this period.

Gemma says that this is not the case.

Using your knowledge of the Large Data Set, give two reasons why Gemma may be correct.

It is known that the mean amount of sugar purchased per person in England in 2014 was 78.9 grams, with a standard deviation of 25.0 grams.

In 2018, a sample of 918 people had a mean of 80.4 grams of sugar purchased per person.

Investigate, at the 5% level of significance, whether the mean amount of sugar purchased per person in England has changed between 2014 and 2018.

Assume that the survey data is a random sample taken from a normal distribution and that the standard deviation has remained the same.

Another test is performed to determine whether the mean amount of fat purchased per person has changed between 2014 and 2018.

At the 10% significance level, the null hypothesis is rejected.

With reference to the 10% significance level, explain why it is not necessarily true that there has been a change.

The table below shows an extract from the Large Data Set.

Year	2011	2012	2013	2014	% change since 2011
Other takeaway food brought home	0	0	0	0	29

Sarah claims that the 29% change since 2011 is incorrect, as there is no change between 2011 and 2014.

Using your knowledge of the Large Data Set to justify your answer, explain whether Sarah’s claim is correct.