Jacob and Natalie are students in Mr. Duke's class. Here are their scores (%) for the last five quizzes:

Question

Jacob: 80, 90, 95, 85, and 70
Natalie: 70, 75, 90, 100, and 95
Who has the better average score? Why?

(1 point)
Responses

Jacob has a better average score with a higher median of 95.
Jacob has a better average score with a higher median of 95.

Natalie has a better average score with a higher mean of 86.
Natalie has a better average score with a higher mean of 86.

Natalie has a better average score with a higher range of 30.
Natalie has a better average score with a higher range of 30.

Natalie scored 100% on one of her quizzes so she must have the better average.
Natalie scored 100% on one of her quizzes so she must have the better average.

Answer 1

To determine who has the better average score, we need to calculate the mean (average) for both Jacob and Natalie.

Jacob's scores: 80, 90, 95, 85, 70

• Sum of scores: 80 + 90 + 95 + 85 + 70 = 420
• Average: 420 / 5 = 84

Natalie's scores: 70, 75, 90, 100, 95

• Sum of scores: 70 + 75 + 90 + 100 + 95 = 430
• Average: 430 / 5 = 86

Now comparing the two averages:

• Jacob's average: 84
• Natalie's average: 86

So, Natalie has the better average score.

Now, let's analyze each of the given response options:

1. "Jacob has a better average score with a higher median of 95." - This is incorrect; Jacob does not have a better average score.
2. "Natalie has a better average score with a higher mean of 86." - This is correct, as Natalie's average is indeed higher.
3. "Natalie has a better average score with a higher range of 30." - The range is not indicative of the average score, so this is misleading.
4. "Natalie scored 100% on one of her quizzes so she must have the better average." - While scoring 100% does contribute to a higher average, this statement alone is not a definitive reasoning.

Therefore, the best response is:

Natalie has a better average score with a higher mean of 86.