Interpret or describe given scatter diagram

8 A random sample of 10 students from a college was chosen. They were asked how much time, \(x\) hours, they spent studying, and how much money, \(\pounds y\), they earned, in a typical week during term time. The results are shown in the scatter diagram.
\includegraphics[max width=\textwidth, alt={}, center]{c4cc2cd8-46bf-448f-b223-92378984bfde-5_544_741_555_242}

1. Comment on the relationship shown by the diagram between hours spent studying and money earned, during term time, by these 10 students. The coordinates of the points in the diagram are \(( 18,23 ) , ( 20,21 ) , ( 23,20 ) , ( 25,19 ) , ( 25,21 )\), \(( 27,18 ) , ( 32,16 ) , ( 38,17 ) , ( 40,16 )\) and \(( 41,23 )\).
2. Find the mean and standard deviation of the number of hours spent per week studying during term time by these 10 students.

11 The scatter diagram below shows data taken from the 2011 UK census for each of the Local Authorities in the North East and North West regions.
The scatter diagram shows the total population of the Local Authority and the proportion of its workforce that travel to work by bus, minibus or coach.
\includegraphics[max width=\textwidth, alt={}, center]{35d8bb6d-ff0f-4590-b13d-46e4869e2587-07_938_1136_664_260}

1. Samuel suggests that, with a few exceptions, the data points in the diagram show that Local Authorities with larger populations generally have higher proportions of workers travelling by bus, minibus or coach. On the diagram in the Printed Answer Booklet draw a ring around each of the data points that Samuel might regard as an exception.
2. Jasper suggests that it is possible to separate these Local Authorities into more than one group with different relationships between population and proportion travelling to work by bus, minibus or coach. Discuss Jasper's suggestion, referring to the data and to how differences between the Local Authorities could explain the patterns seen in the diagram.
   [0pt] [3]

13 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.
\includegraphics[max width=\textwidth, alt={}, center]{40d40a0b-5b33-4940-b15b-ee03e1291f61-10_1038_1122_683_242}

1. Most of the points in the diagram lie on or near the line with equation \(x + y = k\), where \(k\) is a constant.
   1. Give a possible value for \(k\).
   2. Hence give an approximate value for the percentage of employees who either worked from home or walked or cycled to work.
2. 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.
   1. 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.
   2. Suggest two kinds of further information which would enable a more reliable answer to be given.
3. 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.
   1. The two LAs share a certain characteristic. Describe, with a justification, this characteristic.
   2. The environments in these two LAs are very different. Describe, with a justification, this difference.
4. A student says that it is difficult to extract detailed information from the scatter diagram. Explain whether you agree with this criticism.

10 Which of the options below best describes the correlation shown in the diagram below?
\includegraphics[max width=\textwidth, alt={}, center]{c8a41c47-bbda-4e91-a7a2-d0bcf6a46f25-12_750_1246_847_395} Tick \(( \checkmark )\) one box.
moderate positive □
strong positive □
moderate negative □
strong negative □

1. Which of the options below best describes the correlation shown in the diagram below?
\includegraphics[max width=\textwidth, alt={}, center]{d1809ec7-dccf-446b-8a1d-f04a4252ebec-05_719_1198_408_340} Tick ( \(\checkmark\) ) one box.
moderate positive □
strong positive
\includegraphics[max width=\textwidth, alt={}, center]{d1809ec7-dccf-446b-8a1d-f04a4252ebec-05_103_109_1407_881}
moderate negative
\includegraphics[max width=\textwidth, alt={}, center]{d1809ec7-dccf-446b-8a1d-f04a4252ebec-05_103_109_1535_881}
strong negative □

1. Which of the options below best describes the correlation shown in the diagram below?
\includegraphics[max width=\textwidth, alt={}, center]{64d3256a-9007-4e8a-86d4-8375c006a4ce-04_721_1196_406_342} Tick ( \(\checkmark\) ) one box.
moderate positive □
strong positive
\includegraphics[max width=\textwidth, alt={}, center]{64d3256a-9007-4e8a-86d4-8375c006a4ce-04_103_109_1407_881}
moderate negative
\includegraphics[max width=\textwidth, alt={}, center]{64d3256a-9007-4e8a-86d4-8375c006a4ce-04_103_109_1535_881}
strong negative □