Outliers

All the students in the year-group took Test 1, but some students missed Test 2.

State the number of students who missed Test 2.

Find an estimate of the number of students whose marks for Test 1 were in the range 45 to 65

inclusive.

The final parts of the graphs are horizontal.

For Test 1, explain what this means about the results.

It is required that the number of students obtaining grade A* should be the same on both tests. The minimum mark for grade A* on Test 2 was 76.

Find the minimum mark for grade A* on Test 1.

A teacher commented that the median marks on both tests were very similar. This suggests that, on average, the levels of difficulty on both tests were about the same.

Use the cumulative frequency diagram to make another comparison between Test 1 and Test

2 about the easier questions on both papers.

The marks for Test 1 are summarised in the table.

Find estimates of the mean and standard deviation of the Test 1 marks.

Use your answers to part (f)(i) to comment on whether there may be any outliers

amongst the Test 1 marks.

The stem-and-leaf diagram shows the heights, in centimetres, of 15 plants.

| 0 | 2 | 1 | 0 | 2 | 4 | 3 | 0 2 4 9 | 4 | 1 2 4 7 9 | 5 | 3 7 | 6 | 2

Key: | 2 | 5 means 25 cm.

Draw a box-and-whisker plot to illustrate the data.

A statistician intends to analyse the data, but wants to ignore any outliers before doing so.

Discuss briefly whether there are any heights in the diagram which the statistician should

ignore.

The scatter diagram uses information about all the Local Authorities (LAs) in the UK, taken from the 2011 census.

For each LA it shows the percentage (x) of employees who used public transport to travel to work and the percentage (y) who used motorised private transport.

“Public transport” includes train, bus, minibus, coach, underground, metro and light rail. “Motorised private transport” includes car, van, motorcycle, scooter, moped, taxi and passenger in a car or van.

Percentage using public transport (x)

Most of the points in the diagram lie on or near the line with equation x + y = k, where k is a constant.

Give a possible value for k.

Hence give an approximate value for the percentage of employees who either worked

from home or walked or cycled to work.

The average amount of fuel used per person per day for travelling to work in any LA is denoted by F.

Consider the two groups of LAs where the percentages using motorised private transport are highest and lowest.

Using only the information in the diagram, suggest, with a reason, which of these two

groups will have greater values of F than the other group.

A student says that it is not possible to give a reliable answer to part (b)(i) without some further information.

Suggest two kinds of further information which would enable a more reliable answer to

be given.

Points A and B in the diagram are the most extreme outliers. Use their positions on the diagram to answer the following questions about the two LAs represented by these two points.

The two LAs share a certain characteristic.

Describe, with a justification, this characteristic.

The environments in these two LAs are very different.

Describe, with a justification, this difference.

A student says that it is difficult to extract detailed information from the scatter diagram.

Explain whether you agree with this criticism.

Zac is planning to write a report on the music preferences of the students at his college. There is a large number of students at the college.

State one reason why Zac might wish to obtain information from a sample of students, rather

than from all the students.

Amaya suggests that Zac should use a sample that is stratified by school year.

Give one advantage of this method as compared with random sampling, in this context.

Zac decides to take a random sample of 60 students from his college. He asks each student how many hours per week, on average, they spend listening to music during term. From his results he calculates the following statistics.

Sundip tells Zac that, during term, she spends on average 30 hours per week listening to music.

Discuss briefly whether this value should be considered an outlier.

Layla claims that, during term, each student spends on average 20 hours per week listening to music. Zac believes that the true figure is higher than 20 hours. He uses his results to carry out a hypothesis test at the 5% significance level.

Assume that the time spent listening to music is normally distributed with standard deviation 4.20 hours.

Carry out the test.

Christa used Pearson’s product-moment correlation coefficient, r, to compare the use of public transport with the use of private vehicles for travel to work in the UK.

Using the pre-release data set for all 348 UK Local Authorities, she considered the following four variables.

Explain, in context, why you would expect strong, positive correlation between x and y.

Explain, in context, what kind of correlation you would expect between a and b.

Suggest what effect this outlier is likely to have on the value of r for the 32 London Boroughs.

Suggest what effect this outlier is likely to have on the value of r for the whole country.

What can you deduce about the area of the London Borough represented by the outlier?

Explain your answer.