Find the relative frequency marginal distribution of transportation method from a t...
Check the final answer first, then review the worked steps.
Problem
Find the relative frequency marginal distribution of transportation method from a table of commuters by commute duration and transportation method. Round to the nearest whole percent.
Answer
Private vehicle: 97% Public transportation: 0% Other: 2%
Step-by-step solution
1. Identify the marginal totals for each transportation method:
From the table, the total number of commuters for each transportation method are:
- Private vehicle: 1887
- Public transportation: 9
- Other: 42
2. Identify the grand total of commuters:
The total number of commuters is given as 1938.
3. Calculate the relative frequency for each transportation method:
To find the relative frequency, divide the marginal total for each transportation method by the grand total and multiply by 100 to express it as a percentage.
- Private vehicle: $$\frac{1887}{1938} \times 100\%$$
- Public transportation: $$\frac{9}{1938} \times 100\%$$
- Other: $$\frac{42}{1938} \times 100\%$$
4. Perform the calculations and round to the nearest whole percent:
- Private vehicle: $$\frac{1887}{1938} \times 100\% \approx 97.368 \%$$
Rounded to the nearest whole percent, this is 97%.
- Public transportation: $$\frac{9}{1938} \times 100\% \approx 0.464 \%$$
Rounded to the nearest whole percent, this is 0%.
- Other: $$\frac{42}{1938} \times 100\% \approx 2.167 \%$$
Rounded to the nearest whole percent, this is 2%.
5. Verify the sum of relative frequencies:
Adding the rounded percentages: $97\% + 0\% + 2\% = 99\%$. The sum is close to 100%, with the slight difference due to rounding.