Inappropriate graph type selection

1 Two students draw graphs to represent the numbers of pairs of shoes owned by members of their class. Andrew produces a bipartite graph, but gets it wrong. Barbara produces a completely correct frequency graph. Their graphs are shown below. \begin{figure}[h] \end{figure} \begin{figure}[h] \end{figure}

1. Draw a correct bipartite graph.
2. How many people are in the class?
3. How many pairs of shoes in total are owned by members of the class?
4. Which points on Barbara's graph may be deleted without losing any information? Charles produces the same frequency graph as Barbara, but joins consecutive points with straight lines.
5. Criticise Charles's graph.

13 The radar diagrams illustrate some population figures from the 2011 census results.
\includegraphics[max width=\textwidth, alt={}, center]{3fdf2b2d-20a9-4d68-b760-57ec529b5893-6_712_764_303_248}
\includegraphics[max width=\textwidth, alt={}, center]{3fdf2b2d-20a9-4d68-b760-57ec529b5893-6_709_757_303_1137} Each radius represents an age group, as follows: The distance of each dot from the centre represents the number of people in the relevant age group.

1. The scales on the two diagrams are different. State an advantage and a disadvantage of using different scales in order to make comparisons between the ages of people in these two Local Authorities.
2. Approximately how many people aged 45 to 59 were there in Liverpool?
3. State the main two differences between the age profiles of the two Local Authorities.
4. James makes the following claim.
   "Assuming that there are no significant movements of population either into or out of the two regions, the 2021 census results are likely to show an increase in the number of children in Liverpool and a decrease in the number of children in Rutland." Use the radar diagrams to give a justification for this claim.

12. 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]{59120894-c480-492b-a304-106ddbadacf0-30_1234_1160_276_255} \begin{table}[h] \end{table}

1. State, with reasons, which of the four Local Authorities is most likely to be a rural area with many hills.
2. 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.
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4. 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. \section*{Increase in percentage of employees travelling to work by various methods} 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.
   • 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.
   • Estimate the percentage of the people in the age range 20 to 65 in 2011 whose data appears in both 2001 and 2011.
   • 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.

4. The radar diagrams illustrate some population figures from the 2011 census results.
\includegraphics[max width=\textwidth, alt={}, center]{c5ea8584-939f-4627-8f81-bac60233d9a3-10_723_776_360_159}
\includegraphics[max width=\textwidth, alt={}, center]{c5ea8584-939f-4627-8f81-bac60233d9a3-10_725_775_358_1055} Each radius represents an age group, as follows: The distance of each dot from the centre represents the number of people in the relevant age group.

1. The scales on the two diagrams are different. State an advantage and a disadvantage of using different scales in order to make comparisons between the ages of people in these two Local Authorities.
2. Approximately how many people aged 45 to 59 were there in Liverpool?
3. State the main two differences between the age profiles of the two Local Authorities.
4. James makes the following claim.
   "Assuming that there are no significant movements of population either into or out of the two regions, the 2021 census results are likely to show an increase in the number of children in Liverpool and a decrease in the number of children in Rutland." Use the radar diagrams to give a justification for this claim.
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7. The table shows information, derived from the 2011 UK census, about the percentage of employees who used various methods of travel to work in four Local Authorities. One of the Local Authorities is a London borough and two are metropolitan boroughs, not in London.

1. Which one of the Local Authorities is a London borough? Give a reason for your answer.
2. Which two of the Local Authorities are metropolitan boroughs outside London? In each case give a reason for your answer.
3. Describe one difference between the public transport available in the two metropolitan boroughs, as suggested by the table.
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10 The table shows information, derived from the 2011 UK census, about the percentage of employees who used various methods of travel to work in four Local Authorities. One of the Local Authorities is a London borough and two are metropolitan boroughs, not in London.

1. Which one of the Local Authorities is a London borough? Give a reason for your answer.
2. Which two of the Local Authorities are metropolitan boroughs outside London? In each case give a reason for your answer.
3. Describe one difference between the public transport available in the two metropolitan boroughs, as suggested by the table.
4. Comment on the availability of public transport in Local Authority B as suggested by the table.

14 Table 1 shows the numbers of usual residents in the age range 0 to 4 in 15 Local Authorities (LAs) in 2001 and 2011. The table also shows the increase in the numbers in this age group, and the same increase as a percentage. \begin{table}[h] \end{table} Fig. 2 shows the increase in each LA in raw numbers, and Fig. 3 shows the percentage increase in each LA. \begin{figure}[h] \end{figure} \begin{figure}[h] \end{figure}

1. The Education Committees in these LAs need to plan for the provision of schools for pupils in their districts.
   1. Explain why, in this context, the increase is more important than the actual numbers.
   2. 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.
   3. State an assumption about the populations needed to make your answer in part (ii) valid.
2. 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.