OCR H240/02 2022 June — Question 10

Exam BoardOCR
ModuleH240/02 (Pure Mathematics and Statistics)
Year2022
SessionJune
TopicMeasures of Location and Spread
TypeClean or interpret large data set structure

10 The table shows the age structure of usual residents of 18 Local Authorities (LAs) in the North West region of the UK in 2011.
Local AuthorityAge 0 to 17Age 18 to 24Age 25 to 64Age 65 and over
A26.20\%9.06\%51.81\%12.92\%
B23.32\%8.99\%52.32\%15.37\%
C22.24\%8.96\%52.56\%16.23\%
D22.67\%8.10\%53.27\%15.96\%
E20.70\%7.77\%54.77\%16.76\%
F18.14\%6.51\%51.13\%24.21\%
G18.96\%14.20\%48.51\%18.33\%
H19.06\%14.79\%52.12\%14.04\%
I25.15\%9.04\%51.16\%14.65\%
J22.93\%8.81\%52.22\%16.04\%
K21.48\%13.98\%50.82\%13.73\%
L23.98\%9.20\%52.26\%14.56\%
M21.67\%11.19\%52.94\%14.19\%
N17.82\%6.01\%51.93\%24.23\%
O22.83\%7.30\%53.86\%16.01\%
P21.76\%8.28\%54.03\%15.93\%
Q21.42\%8.43\%53.90\%16.25\%
R18.61\%7.33\%49.35\%24.71\%
\section*{Percentage of residents}
  1. 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.
    1. An LA that includes a university
    2. An LA that attracts young couples to live
    3. An LA that attracts retired people to live
  2. Using your answers to part (a), identify the following.
    1. Four LAs that might include a university
    2. Three LAs that might be attractive to retired people
  3. 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.
  4. 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.
  5. 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".