Data presentation and interpretation

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.

One researcher suggests that, for each of the LAs, they should compare the sum of the data for 2001 for Age 15 to 19 with the data for 2011 for Age 25 to 29.

Explain why this comparison is relevant.

The census data also includes data for the following age ranges:

Explain why none of these data ranges are helpful in this context.

The data for one of these four LAs show that some of the 0 to 4 year olds living in that LA in 2001 are definitely no longer living there in 2011.

Explain which LA this is.

One of the researchers says that there has been little movement in or out of Bournemouth between 2001 and 2011 for those who were aged 5 to 7 in 2001.

Use values from the table to show that this statement is not contradicted by the data.

Explain why the statement is not necessarily correct.

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.

The table shows the age structure of usual residents of 18 Local Authorities (LAs) in the North West region of the UK in 2011.

Without reference to any other columns, explain how you would use only the columns for the age ranges 0 to 17 and 18 to 24 to decide whether an LA might be one of the following.

An LA that includes a university

An LA that attracts young couples to live

An LA that attracts retired people to live

Using your answers to part (a), identify the following.

Four LAs that might include a university

Three LAs that might be attractive to retired people

Explain why your answer to part (b)(ii), based only on the columns for the age ranges 0 to 17

and 18 to 24, may not be reliable.

The lower quartile, median and upper quartile of the percentages in the column “Age 65 and over” are 14.56%, 15.99% and 16.76% respectively.

Use this information to comment on your answers to part (b)(ii) and part (c).

In a magazine article, a councillor plans to describe a typical LA in the North West region. He wants to quote the average percentage of residents aged 65 or over.

The mean of the percentages in the column “Age 65 and over” is 16.90%.

Use this information, and the information given in part (d), to explain whether the median or

the mean better represents the data in the column “Age 65 and over”.

The four pie charts illustrate the numbers of employees using different methods of travel in four Local Authorities in 2011.

Local Authority A
Local Authority B

Local Authority C
Local Authority D

State, with reasons, which of the four Local Authorities is most likely to be a rural area with

Explain why pie charts are more suitable for answering part (a) than bar charts showing the

same data.

Two of the Local Authorities represent urban areas.

State with a reason which two Local Authorities are likely to be urban.

One urban Local Authority introduced a Park-and-Ride service in 2006. Users of this service drive to the edge of the urban area and then use buses to take them into the centre of the area. A student claims that a comparison of the corresponding pie charts for 2001 (not shown) and 2011 would enable them to identify which Local Authority this was.

State with a reason whether you agree with the student.

The histogram shows information about the numbers of cars in five different price ranges, sold in one year at a car showroom.

It is given that 66 cars in the price range £10 000 to £20 000 were sold.

Find the number of cars sold in the price range £50 000 to £90 000.

State the units of the frequency density.

Suggest one change that the management could make to the diagram so that it would provide

more information.

Estimate the number of cars sold in the price range £50 000 to £60 000.

The Education Committees in these LAs need to plan for the provision of schools for pupils in their districts.

Explain why, in this context, the increase is more important than the actual numbers.

In which of the following LAs was there likely to have been the greatest need for extra teachers in the years following 2011: Bolton, Sefton, Tameside or Wigan?

Give a reason for your answer.

State an assumption about the populations needed to make your answer in part (ii) valid.

In two of the 15 LAs the proportion of young families is greater than in the other 13 LAs. Suggest, using only data from Fig. 2 and Fig. 3 and/or Table 1, which two LAs these are most

likely to be.