Table 1 shows the results of measuring the petrol consumption of a car over 90 trials. $$ \begin{array}{lc} \hline \text { Miles per gallon } & \text { Frequency } \\ \hline 42 & 17 \\ 43 & 18 \\ 44 & 12 \\ 45 & 20 \\ 46 & 23 \\ \hline \end{array} $$ (a) Calculate the mean consumption. (b) Calculate the standard deviation.

To compute the mean consumption, first multiply the miles per gallon (mpg) by its respective frequency and then sum the products. Next, divide the sum by the total number of trials (90). Mean Consumption = \(\frac{\sum{(mpg * frequency)}}{total\ trials}\) Mean Consumption = \(\frac{(42*17) + (43*18) + (44*12) + (45*20) + (46*23)}{90}\) Now, compute the mean consumption: Mean Consumption = \(\frac{(714) + (774) + (528) + (900) + (1058)}{90}\) Mean Consumption = \(\frac{3974}{90}\)= 44.16 mpg

To compute the standard deviation, first calculate the variance, which is the average squared deviation from the mean. Then, take the square root of the variance to obtain the standard deviation. Variance = \(\frac{\sum{(mpg - mean)^2 * frequency}}{total\ trials}\) Variance = \(\frac{(42-44.16)^2 * 17 + (43-44.16)^2 * 18 + (44-44.16)^2 * 12 + (45-44.16)^2 * 20 + (46-44.16)^2 * 23}{90-1}\) Now, compute the variance: Variance = \(\frac{(4.66^2 * 17) + (1.16^2 * 18) + (0.16^2 * 12) + (0.84^2 * 20) + (1.84^2 * 23)}{89}\) Variance = \(\frac{(381.21) + (25.37) + (0.31) + (14.11) + (77.66)}{89}\) Variance = \(\frac{498.66}{89}\)= 5.60 Finally, compute the standard deviation by taking the square root of the variance: Standard Deviation = \(\sqrt{5.60}\)= 2.37 mpg