Evaluate claims about large data set

1. Ming is studying the large data set for Perth in 2015

He intended to use all the data available to find summary statistics for the Daily Mean Air Temperature, \(x { } ^ { \circ } \mathrm { C }\).
Unfortunately, Ming selected an incorrect variable on the spreadsheet.
This incorrect variable gave a mean of 5.3 and a standard deviation of 12.4

1. Using your knowledge of the large data set, suggest which variable Ming selected. The correct values for the Daily Mean Air Temperature are summarised as $$n = 184 \quad \sum x = 2801.2 \quad \sum x ^ { 2 } = 44695.4$$
2. Calculate the mean and standard deviation for these data. One of the months from the large data set for Perth in 2015 has
   • mean \(\bar { X } = 19.4\)
   • standard deviation \(\sigma _ { x } = 2.83\) for Daily Mean Air Temperature.
   • Suggest, giving a reason, a month these data may have come from.

In lines 101 and 102, the text says "The total number of transactions for those who responded has been estimated as 100 000 for the \(3\frac{1}{2}\) years covered by the survey." Estimate the number of transactions per person per day that would give this figure. [2]

The survey described in the article was based on a small sample. State one conclusion which is unlikely to be influenced by the size of the sample. [1]

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. \includegraphics{figure_14} Fig. 2 shows the increase in each LA in raw numbers, and Fig. 3 shows the percentage increase in each LA. \includegraphics{figure_14_2} \includegraphics{figure_14_3}

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. [1]
   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. [2]
   3. State an assumption about the populations needed to make your answer in part (ii) valid. [1]
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. [2]

The table below shows an extract from the Large Data Set.

Year	2011	2012	2013	2014	\% change since 2011
Other takeaway food brought home	0	0	0	0	\(-29\)

Sarah claims that the \(-29\%\) change since 2011 is incorrect, as there is no change between 2011 and 2014. Using your knowledge of the Large Data Set to justify your answer, explain whether Sarah's claim is correct. [3 marks]