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
Mean Absolute Deviation (MAD) of Jacob's scores is 7.2

Mean Absolute Deviation (MAD) of Natalie's scores is 10.8

Who has the more consistent scores? Choose the two statements that best answer this question.

(2 points)
Responses

Jacob's scores are more consistent since his Range in scores is smaller.
Jacob's scores are more consistent since his Range in scores is smaller.

Natalie's scores are more consistent since her Range in scores is larger.
Natalie's scores are more consistent since her Range in scores is larger.

Natalie's scores are more consistent since her Mean Absolute Deviation (MAD) is larger.
Natalie's scores are more consistent since her Mean Absolute Deviation (MAD) is larger.

Jacob's scores are more consistent since his Mean Absolute Deviation (MAD) is smaller.
Jacob's scores are more consistent since his Mean Absolute Deviation (MAD) is smaller.
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Answer 1

To determine who has the more consistent scores, we can analyze the Mean Absolute Deviation (MAD) and the Range of scores for both Jacob and Natalie.

1. Jacob's Mean Absolute Deviation (MAD): 7.2
2. Natalie's Mean Absolute Deviation (MAD): 10.8

A smaller MAD indicates that the scores are closer to the mean and hence more consistent. Therefore, Jacob's scores are more consistent because his MAD (7.2) is smaller than Natalie's MAD (10.8).

Next, let's look at the range:

• Jacob's scores: 70 to 95, giving a range of 95 - 70 = 25.
• Natalie's scores: 70 to 100, giving a range of 100 - 70 = 30.

While Jacob's range is smaller (25 as opposed to 30), the MAD is a more reliable measure of consistency. Thus, we can conclude that Jacob is more consistent overall based on both MAD and range.

Now, let's choose the two statements that best answer the question:

1. Jacob's scores are more consistent since his Mean Absolute Deviation (MAD) is smaller.
2. Jacob's scores are more consistent since his Range in scores is smaller.

These two statements correctly indicate that Jacob demonstrates more consistent performance in his quiz scores compared to Natalie.