Question
What inference can you make by comparing the measures of center?
Finish Times of 30 Runners
in the 100-meter Dash
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Every runner ran faster last year as compared to this year.
Most runners ran faster last year, on average, as compared to this year.
The runners ran faster this year, on average, as compared to last year.
Every runner ran faster this year as compared to last year.
Finish Times of 30 Runners
in the 100-meter Dash
Mean MAD
Last Year 16.2 s 1.2
This Year 14.7 s 1.9
Every runner ran faster last year as compared to this year.
Most runners ran faster last year, on average, as compared to this year.
The runners ran faster this year, on average, as compared to last year.
Every runner ran faster this year as compared to last year.
Answers
GPT-4o mini
To accurately compare the performance of runners over the two years, we can look at the provided measures of center (mean) for each year:
- Last Year: Mean finish time = 16.2 seconds
- This Year: Mean finish time = 14.7 seconds
Since the mean finish time this year (14.7 s) is lower than last year's mean finish time (16.2 s), we can infer that, on average, the runners ran faster this year compared to last year.
Now let's look at the options to see which one accurately represents this conclusion:
1. **Every runner ran faster last year as compared to this year.** - This is not correct, as the average indicates that runners performed better this year.
2. **Most runners ran faster last year, on average, as compared to this year.** - This is also not accurate for the same reason as above.
3. **The runners ran faster this year, on average, as compared to last year.** - This is correct, as it aligns with the conclusion drawn from the mean finish times.
4. **Every runner ran faster this year as compared to last year.** - This cannot be concluded from the mean, as it is possible for some runners to have run slower this year while the average still decreased.
Based on the analysis of this data, the best inference to make is:
**The runners ran faster this year, on average, as compared to last year.**
- Last Year: Mean finish time = 16.2 seconds
- This Year: Mean finish time = 14.7 seconds
Since the mean finish time this year (14.7 s) is lower than last year's mean finish time (16.2 s), we can infer that, on average, the runners ran faster this year compared to last year.
Now let's look at the options to see which one accurately represents this conclusion:
1. **Every runner ran faster last year as compared to this year.** - This is not correct, as the average indicates that runners performed better this year.
2. **Most runners ran faster last year, on average, as compared to this year.** - This is also not accurate for the same reason as above.
3. **The runners ran faster this year, on average, as compared to last year.** - This is correct, as it aligns with the conclusion drawn from the mean finish times.
4. **Every runner ran faster this year as compared to last year.** - This cannot be concluded from the mean, as it is possible for some runners to have run slower this year while the average still decreased.
Based on the analysis of this data, the best inference to make is:
**The runners ran faster this year, on average, as compared to last year.**