Step 1 :First, calculate the total frequency, which is the sum of all the frequencies. In this case, the total frequency is 80.
Step 2 :Next, calculate the relative frequency for each category by dividing the frequency of each category by the total frequency. The relative frequencies are 40%, 31.25%, 5%, 13.75%, and 10% for American cars, Japanese cars, English cars, Other European cars, and Motorcycles respectively.
Step 3 :Then, calculate the cumulative frequency by adding up the frequencies as we move down the table. The cumulative frequencies are 32, 57, 61, 72, and 80 for American cars, Japanese cars, English cars, Other European cars, and Motorcycles respectively.
Step 4 :Finally, fill in the frequency table with the calculated values. The completed frequency table is: \begin{tabular}{lccc} Category of vehicle & Frequency & \begin{tabular}{c} Relative \ Frequency \end{tabular} & \begin{tabular}{c} Cumulative \ Frequency \end{tabular} \\ \hline American cars & 32 & $40 \%$ & 32 \\ Japanese cars & 25 & $31.25 \%$ & 57 \\ English cars & 4 & $5 \%$ & 61 \\ Other European cars & 11 & $13.75 \%$ & 72 \\ Motorcycles & 8 & $10 \%$ & 80 \\ \hline Total & 80 & $100 \%$ & 80 \\ \end{tabular}
Step 5 :\(\boxed{\text{The completed frequency table is:}}\) \begin{tabular}{lccc} Category of vehicle & Frequency & \begin{tabular}{c} Relative \ Frequency \end{tabular} & \begin{tabular}{c} Cumulative \ Frequency \end{tabular} \\ \hline American cars & 32 & $40 \%$ & 32 \\ Japanese cars & 25 & $31.25 \%$ & 57 \\ English cars & 4 & $5 \%$ & 61 \\ Other European cars & 11 & $13.75 \%$ & 72 \\ Motorcycles & 8 & $10 \%$ & 80 \\ \hline Total & 80 & $100 \%$ & 80 \\ \end{tabular}