First, let's define the problem clearly. We need to compare the likelihood of a male preferring running to the likelihood of a female preferring running, given the total percentages of males and females, respectively, who prefer running and their total populations.
### Step-by-Step Solution
1. Identify the given percentages:
- Males:
- Cycling: 15%
- Running: 13%
- Swimming: 21%
- Total: 49%
- Females:
- Cycling: 12%
- Running: 16%
- Swimming: 23%
- Total: 51%
2. Calculate the conditional relative frequency for males preferring running:
- Here, we use the percentage of males who prefer running compared to the total number of males.
- The percentage of males who prefer running is 13%.
- The total percentage of males is 49%.
- Conditional relative frequency for males preferring running:
[tex]\[
\text{Male Conditional Running} = \frac{13\%}{49\%}
\][/tex]
- Converting percentages to decimals for easier calculation:
[tex]\[
\text{Male Conditional Running} = \frac{0.13}{0.49} \approx 0.27 \, (\text{rounded to 2 decimal places})
\][/tex]
3. Calculate the conditional relative frequency for females preferring running:
- Similarly, we use the percentage of females who prefer running compared to the total number of females.
- The percentage of females who prefer running is 16%.
- The total percentage of females is 51%.
- Conditional relative frequency for females preferring running:
[tex]\[
\text{Female Conditional Running} = \frac{16\%}{51\%}
\][/tex]
- Converting percentages to decimals for easier calculation:
[tex]\[
\text{Female Conditional Running} = \frac{0.16}{0.51} \approx 0.31 \, (\text{rounded to 2 decimal places})
\][/tex]
4. Compare the conditional relative frequencies:
- For males preferring running: [tex]\( \approx 0.27 \)[/tex]
- For females preferring running: [tex]\( \approx 0.31 \)[/tex]
Therefore, comparing both values, we get that the conditional relative frequencies of a male preferring running to a female preferring running are approximately [tex]\(0.27\)[/tex] to [tex]\(0.31\)[/tex].
