To determine which scatterplot correctly represents the average 5K marathon times for runners of various ages based on the provided data, we need to first understand the data points given in the table:
- For age 24, the time is 32.75 minutes
- For age 29, the time is 33.63 minutes
- For age 34, the time is 34.84 minutes
- For age 39, the time is 35.33 minutes
- For age 44, the time is 35.23 minutes
- For age 49, the time is 36.16 minutes
Now, let's analyze the provided scatterplots with respect to the ages and times:
-
The first option suggests points approximately at:
- (24, 33)
- (29, 33.5)
- (34, 35)
- (39, 35.5)
- (44, 35.5)
- (49, 36) These values seem slightly off since they don't precisely match the provided times.
-
The second option has points that do not correspond to the data provided (ages 33, 34, etc.).
-
The third option shows points around:
- (22, 32.5)
- (32, 33.5)
- (34, 34.5)
- (42, 35)
- (44, 35)
- (49, 36) These ages and times also do not match our data set.
-
The fourth option features points that also do not correspond with the data provided (ages 33, 32, 34.5, etc.)
After reviewing all the options and their corresponding data points, none of the described scatterplots match the specified averages perfectly.
However, based on the values closest to the actual data provided, the first scatterplot is the best approximation despite being slightly off as it at least provides the points in a similar age-time framework.
If you were to construct the scatterplot correctly based on the actual data:
- (24, 32.75)
- (29, 33.63)
- (34, 34.84)
- (39, 35.33)
- (44, 35.23)
- (49, 36.16)
You would see that the time increases with age, which is typical in such datasets. Please choose the first option as the closest representation if you had to select one based on provided characteristics in the question.