Question $2-18$ marks

Adriane is comparing the $C{O}_2$ outputs of the top $19$ energy suppliers in $2017$ with the same energy suppliers in $2021.$ The data are recorded in Table $1.$

Table $1C{O}_2$ output of Energy suppliers in $2017$ and $2021$

$11$

$\backslash$table$[[\backslash$table$[[C{O}_2$ output $2017$ to nearest whole number$],[($g per kWh $)]],\backslash$table$[[C{O}_2$ output $2021$ to nearest whole number$],[($g per kWh $)]]],[252,0],[0,0],[234,392],[298,74],[0,0],[84,42],[111,0],[0,0],[132,188],[127,0],[0,62],[298,244],[252,0],[280,0],[0,188],[298,0],[298,277],[337,392],[254,194]]$

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$($a$)($i$)$ Enter the values from Table $1$ above into two new lists in Dataplotter. Copy and complete the table below, rounding values,

where necessary, to one decimal place. $($The mean, rounded to where necessary, to one decimal place. $($The mean, rounded to one

decimal place, is given for you as a check that you have entered the data correctly.$)$

$\backslash$table$[[,\backslash$table$[[C{O}_2$ output $2017],[($g per kWh$)]],\backslash$table$[[C{O}_2$ output $2021],[($g per kWh $)]]],[$Min$,,],[$Median$,,],[$Max$,,],[$Mean$,171\mathrm{.}3,108\mathrm{.}1],[$SD$,,],[$IQ range,,$],[$Range$,,]]$

$($ii$)$ Use the two measures of location to say which year had a greater $C{O}_2$ output per kWh on average

$($iii$)$ Use all three measures of spread to say which year had the greater

variability in $C{O}_2$ output per kWh $.$ Create boxplots for fer kWh $.$

$($b$)($i$)$ Create boxplots for these two datasets $($either drawn by hand or using Dataplotter, or a suitable computer package$),$ and include

them with the rest of your EMA. Include information required for drawing boxplots as set out in Subsection $1\mathrm{.}2$ of Unit $11.$

The summary values can be displayed on the boxplots themselves or in a table to the side of the chart, as they appear in Dataplotter.

$($ii$)$ Use the boxplot for the responses from the year $2021$ to say whether the data are symmetric or skewed. If the data are skewed,

then state whether they are skewed to the left or skewed then state whether they are skewed to the left or skewed to the dataset for the year $2021?$ iii$)$ Adriane tries to summarise what the boxplots are telling her. Are the following statements true or false? In each case justify your answer

$(1)$ In $2017$ about three$-$quarters of the top $19$ energy companies produced more than $234$ g of $C{O}_2$ output per kWh more than $42$ g of $C{O}_2$ output per kWh $.$

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$($c$)$ Adriane also looks at the output of waste from nuclear energy generation for the same $19$ energy suppliers for

summary of the data is recorded in Table $2.$

Table $2$ Output of waste from nuclear energy generation of Energy

suppliers in $2017$ and $2021$

$\backslash$table$[[,\backslash$table$[[2017$ high$-$level nuclear waste$],[($mg per kWh $)]],\backslash$table$[[2021$ high$-$level nuclear waste$],[($mg per kWh $)]]],[$Min$,0,0],[$Median$,0\mathrm{.}38,0],[$Max$,5\mathrm{.}4,4\mathrm{.}3],[$Mean$,0\mathrm{.}66,0\mathrm{.}51],[$SD$,1\mathrm{.}19,1\mathrm{.}01],[$IQ range,$0\mathrm{.}79,0\mathrm{.}69],[$Range$,5\mathrm{.}4,4\mathrm{.}3]]$

She creates dotplots for the nuclear waste data, shown in Figure $1,$ but forgets to label them. Which dotplot represents which year? Explain your answer.

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