Question

An elementary school class ran 1 mile in an average of 11 minutes with a standard deviation of 3 minutes. Rachel, a student in the class, ran 1 mile in 8 minutes. A junior high school class ran 1 mile in an average of 9 minutes, with a standard deviation of 2 minutes. Kenji, a student in the class, ran 1 mile in 8.5 minutes. A high school class ran 1 mile in an average of 7 minutes with a standard deviation of 4 minutes. Nedda, a student in the class, ran 1 mile in 8 minutes.

Required:
a. Why is Kenji considered a better runner than Nedda, even though Nedda ran faster than he?
b. Who is the fastest runner with respect to his or her class? Explain why.

Answer 1

Explanation:

a.

Kenji ran faster than the class average by 0.25 of a standard deviation while Nedda was slower than the average in her class.

b.

Rachel: average - 1st deviation

Kenji: average - 0.25 standard deviation

Nedda: slower than average so it's definitely not her.

Since Rachel is faster than the average and differs by the most standard deviations compared with Kenji,

So, Rachel is the faster one.