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.
   • 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.

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.

5. In March 2020, the coronavirus pandemic caused major disruption to the lives of individuals across the world. A newspaper published the following graph from the \href{http://gov.uk}{gov.uk} website, along with an article which included the following excerpt.
"The daily number of vaccines administered continues to fall. In order to get control of the virus, we need the number of people receiving a second dose of the vaccine to keep rocketing. The fear is it will start to drop off soon, which will leave many people still unprotected." \begin{figure}[h] \end{figure}

1. By referring to the graph, explain how the quote could be misleading.
   The daily numbers of second dose vaccines, in thousands, over the period April 1st 2021 to May 31st 2021 are shown in the table below.

   Daily number of 2nd dose vaccines (1000s)	Midpoint \(x\)	Frequency \(f\)	Percentage
   \(0 \leqslant v < 100\)	50	2	3.3
   \(100 \leqslant v < 200\)	150	8	13.1
   \(200 \leqslant v < 300\)	250	10	16.4
   \(300 \leqslant v < 400\)	350	13	21.3
   \(400 \leqslant v < 500\)	450	26	\(42 \cdot 6\)
   \(500 \leqslant v < 600\)	550	2	3.3
   Total		61	100

2. 1. Calculate estimates of the mean and standard deviation for the daily number of second dose vaccines given over this period. You may use \(\sum x ^ { 2 } f = 8272500\). [4]
   2. Comment on the skewness of these data.
      A second graph in the article shows the number of people receiving a third dose of the vaccine. This graph has a repeated pattern of rising then falling. An extract is shown below. \begin{figure}[h]
      \captionsetup{labelformat=empty} \caption{Number of people (millions) who received 3rd dose vaccinations daily in the UK, by report date} \includegraphics[alt={},max width=\textwidth]{d9ef2033-bf8b-4aec-bc88-34dbc8b9c208-14_556_1115_571_466}
      \end{figure}
3. Give a possible reason for the pattern observed in this graph.
   Another extract shows the number of people who received the third dose of the vaccine between 27th March 2022 and 25th April 2022. \begin{figure}[h]
   \captionsetup{labelformat=empty} \caption{Number of people (1000s) who received 3rd dose vaccinations daily in the UK, by report date} \includegraphics[alt={},max width=\textwidth]{d9ef2033-bf8b-4aec-bc88-34dbc8b9c208-15_537_1246_571_406}
   \end{figure}
4. State, with a reason, whether or not you think the data for April 15th to April 18th are incorrect.

3. Researchers investigated the change in the numbers of people in employment using underground, metro, light rail or tram (UMLRT) between 2001 and 2011. The data are combined for those Local Authorities (LAs) with UMLRT stations into five regions: Birmingham, Liverpool, Manchester, Sheffield and Rotherham, and Tyne and Wear. Fig. 1 shows the total numbers of people in employment in those LAs. Fig. 2 shows the total numbers of people in employment who use UMLRT in those LAs. \begin{figure}[h] \end{figure} \begin{figure}[h] \end{figure}

1. Use these charts to explain which of Birmingham and Liverpool has the larger proportion of people in employment who used UMLRT in 2011. One of the researchers says, "Between 2001 and 2011, the increase in the number of people in employment who use UMLRT is greatest in Tyne and Wear." Sam says, "But what matters more is which region has the greatest increase in the proportion of people in employment who use UMLRT."
2. Give a reason why the planners responsible for the building of trains and the maintenance of infrastructure might disagree with Sam.
3. Explain whether those responsible for encouraging the greater use of public transport would agree with Sam.
4. The charts are compiled from data in the Large Data Set by using those LAs which contain UMLRT stations in each region. Explain a disadvantage of using these data.