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Question 141 - DA0-001 discussion

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Randy scored 76 on a math test, Katie scored 86 on a science test, Ralph scored 80 on a history test, and Jean scored 80 on an English test. The table below contains the mean and standard deviation of the scores for each of the courses:

Using this information, which of the following students had the BEST score?

A.
Randy
Answers
A.
Randy
B.
Katie
Answers
B.
Katie
C.
Ralph
Answers
C.
Ralph
D.
Jean
Answers
D.
Jean
Suggested answer: B

Explanation:

To compare the students' scores, we need to standardize them by using the z-score formula, which is:

z = (x - µ) / σ

where x is the raw score, µ is the mean, and s is the standard deviation. The z-score tells us how many standard deviations a score is above or below the mean. A higher z-score means a better score relative to the average.

Using the table, we can calculate the z-scores for each student as follows:

Randy: z = (76 - 70) / 2 = 3 Katie: z = (86 - 80) / 3 = 2 Ralph: z = (80 - 75) / 2 = 2.5 Jean: z = (80 - 90) / 1 = -10

The student with the highest z-score is Randy, with a z-score of 3. This means that Randy scored 3 standard deviations above the mean in math, which is the best performance among the four students. Therefore, the correct answer is A.

Reference: Comparing with z-scores (video) | Z-scores | Khan Academy, 17 Important Data Visualization Techniques | HBS Online

asked 02/10/2024
Bhavya AGGARWAL
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