Problem
13 The table below is an extract from the Large Data Set. \begin{tabular}{|c|c|c|c|c|c|} \hline $\begin{array}{c}\text { Propulsion } \\ \text { Type }\end{array}$ & Region & Engine Size & Mass & $\mathbf{C O}_{2}$ & $\begin{array}{c}\text { Particulate } \\ \text { Emissions }\end{array}$ \\ \hline 2 & London & 1896 & 1533 & 154 & 0.04 \\ \hline 2 & North West & 1896 & 1423 & 146 & 0.029 \\ \hline 2 & North West & 1896 & 1353 & 138 & 0.025 \\ \hline 2 & South West & 1998 & 1547 & 159 & 0.026 \\ \hline 2 & London & 1896 & 1388 & 138 & 0.025 \\ \hline 2 & South West & 1896 & 1214 & 130 & 0.011 \\ \hline 2 & South West & 1896 & 1480 & 146 & 0.029 \\ \hline 2 & South West & 1896 & 1413 & 146 & 0.024 \\ \hline 2 & South West & 2496 & 1695 & 192 & 0.034 \\ \hline 2 & South West & 1422 & 1251 & 122 & 0.025 \\ \hline 2 & South West & 1995 & 2075 & 175 & 0.034 \\ \hline 2 & London & 1896 & 1285 & 140 & 0.036 \\ \hline 2 & North West & 1896 & 0 & 146 & \\ \hline \end{tabular} 13 (a) (i) Calculate the mean and standard deviation of $\mathrm{CO}_{2}$ emissions in the table. [2 marks]
Solution
Step 1 ：Extract the CO2 emissions data from the table: \(\{154, 146, 138, 159, 138, 130, 146, 146, 192, 122, 175, 140, 146\}\)
Step 2 ：Calculate the mean of CO2 emissions: \(\frac{154+146+138+159+138+130+146+146+192+122+175+140+146}{13} \approx 148.62\)
Step 3 ：Calculate the standard deviation of CO2 emissions: \(\sqrt{\frac{(154-148.62)^2+(146-148.62)^2+\cdots+(146-148.62)^2}{12}} \approx 17.75\)
Step 4 ：\(\boxed{\text{The mean CO2 emissions is approximately 148.62 and the standard deviation is approximately 17.75}}\)
