Misinterpretation of data in graphs

13 The four pie charts illustrate the numbers of employees using different methods of travel in four Local Authorities in 2011. \includegraphics[max width=\textwidth, alt={}, center]{7298e7b9-ad52-480c-bc2b-8289aeab9ebb-10_1131_1077_347_242}

1. State, with reasons, which of the four Local Authorities is most likely to be a rural area with many hills.
2. Explain why pie charts are more suitable for answering part (a) than bar charts showing the same data.
3. Two of the Local Authorities represent urban areas.
   1. State with a reason which two Local Authorities are likely to be urban.
   2. 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.

1. Jiang is studying the variable Daily Mean Pressure from the large data set.

He drew the following box and whisker plot for these data for one of the months for one location using a linear scale but

• he failed to label all the values on the scale
• he gave an incorrect value for the median \includegraphics[max width=\textwidth, alt={}, center]{08e3b0b0-2155-4b37-83e3-343c317ca10c-09_248_1264_573_402}

Daily Mean Pressure (hPa)
Using your knowledge of the large data set, suggest a suitable value for

1. the median,
2. the range.
   (You are not expected to have memorised values from the large data set. The question is simply looking for sensible answers.)
   1. Jiang is studying the variable Daily Mean Pressure from the large data set.
   He drew the following box and whisker plot for these data for one of the months for one nong asing at
   • he gave an incorrect value for the median "
   Using your knowledge of the large data set, suggest a suitable value for
3. the median,
   " \includegraphics[max width=\textwidth, alt={}, center]{08e3b0b0-2155-4b37-83e3-343c317ca10c-09_42_31_1213_1304}
   "

1. Keith is studying the variable Daily Mean Wind Direction, in degrees, from the large data set.

Keith summarised the data for Camborne from 1987 into 4 directions \(A , B , C\) and \(D\) representing North, South, East and West in some order.

1. Using your knowledge of the large data set state, giving a reason, which direction \(A\) represents. The entry for Hurn on 27th September 1987 was 999
2. State, giving a reason, what Keith should do with this value.

10 The table shows extracts from the "Method of travel by LA" tabs for 2001 and 2011 in the large data set.

1. In one of these four LAs a new tram system was opened in 2004. Suggest, with a reason taken from the data, which LA this could have been.
2. Julian suggests that the figures for "Bus, minibus or coach" for LA1 show that some new bus routes were probably introduced in this LA between 2001 and 2011. Use data from the table to comment on this suggestion.
3. In one of these four LAs a congestion charge on vehicles was introduced in 2003. Suggest, with a reason taken from the data, which LA this could have been.

10 The table shows the increases, between 2001 and 2011, in the percentages of employees travelling to work by various methods, in the Local Authorities (LAs) in the North East region of the UK. The first two digits of the Geography code give the type of each of the LAs:
06: Unitary authority
07: Non-metropolitan district
08: Metropolitan borough

1. In what type of LA are the largest increases in percentages of people travelling by underground, metro, light rail or tram?
2. Identify two main changes in the pattern of travel to work in the North East region between 2001 and 2011. Now assume the following.

9 The pre-release material contains information concerning the median income of taxpayers in different areas of London. Some of the data for Camden is shown in the table below. The years quoted in this question refer to the end of the financial years used in the pre-release material. For example, the year 2004 in the table refers to the year 2003/04 in the pre-release material.

1. Explain whether these data are a sample or a population of Camden taxpayers. A time series for the data is shown below. \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Median income of taxpayers in Camden 2004-2011} \includegraphics[alt={},max width=\textwidth]{11788aaf-98fb-4a78-8a40-a40743b1fe15-07_624_1469_950_242}
   \end{figure} The LINEST function on a spreadsheet is used to formulate the following model for the data: \(I = 1115 Y - 2212950\), where \(I =\) median income of taxpayers in \(\pounds\) and \(Y =\) year.
2. Use this model to find an estimate of the median income of taxpayers in Camden in 2009.
3. Give two reasons why this estimate is likely to be close to the true value. The median income of taxpayers in Croydon in 2009 is also not available.
4. Use your knowledge of the pre-release material to explain whether the model used in part (b) would give a reasonable estimate of the missing value for Croydon.

The table below is an extract from the Large Data Set, showing the purchased quantities of fats and oils for the South East of England in 2014.

Description	Purchased quantity
Butter	42
Soft margarine	16
Olive oil	17
Other vegetable and salad oils	28

Kim claims that more olive oil was purchased in the South East than soft margarine. Explain why Kim may be incorrect. [2 marks]

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. [2 marks]

The table shows the increases, between 2001 and 2011, in the percentages of employees travelling to work by various methods, in the Local Authorities (LAs) in the North East region of the UK. \includegraphics{figure_4} The first two digits of the Geography code give the type of each of the LAs: 06: Unitary authority 07: Non-metropolitan district 08: Metropolitan borough

1. In what type of LA are the largest increases in percentages of people travelling by underground, metro, light rail or tram? [1]
2. Identify two main changes in the pattern of travel to work in the North East region between 2001 and 2011. [2]

Now assume the following.

• The data refer to residents in the given LAs who are in the age range 20 to 65 at the time of each census.
• The number of people in the age range 20 to 65 who move into or out of each given LA, or who die, between 2001 and 2011 is negligible.

1. Estimate the percentage of the people in the age range 20 to 65 in 2011 whose data appears in both 2001 and 2011. [2]
2. In the light of your answer to part (c), suggest a reason for the changes in the pattern of travel to work in the North East region between 2001 and 2011. [1]