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Below are ten scores for two different students. Students have a choice: they can take the median of their scores as their final grade, or they can take the mean of their scores as a final grade. Scores are rounded to the nearest whole number. For each student tell which option would result in the highest grade.

Student A: 25, 78, 80, 82, 85, 86, 88, 89, 96, 99
Student B: 71, 77, 77, 79, 79, 80, 88, 89, 91, 96
Find the median and mean for both students.

User Nov Matake
by
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2 Answers

10 votes
10 votes

Answer:

Student A's median and Student B's mean would result in the highest grade.

Explanation:

How to find the mean:

The mean is the average.

Therefore, you must add all numbers listed, then divide the added numbers by the amount of numbers you added together. Lastly, as instructed round to the nearest whole number.

- Student A : Mean = 81

Step 1 : 25+78+80+82+85+86+88+89+96+99 = 808

Step 2: 808 ÷ 10 = 80.8

Step 3: 80.8 ---> 81

- Student B: Mean = 83

Step 1: 71+77+77+79+79+80+88+89+91+96 = 827

Step 2: 827 ÷ 10 = 82.7

Step 3: 82.7 ---> 83

How to find the median:

The median is the middle number in a sorted list of numbers.

Therefore, you list all of the numbers from least to greatest. Then, you get rid of a number from each side until you finally get to the center number. If there are two numbers left in the center you then find the mean(average) of those numbers.

- Student A: Median = 86

Step 1: Knock off a number from each side until you reach the center number(s)

25, 78, 80, 82, 85, 86, 88, 89, 96, 99 ---> 85, 86

Step 2: Find the mean(average) of the two central numbers

85 + 86 = 171 ---> 171 ÷ 2 = 85.5

Step 3: Round your answer

85.5 ---> 86

- Student B: Median = 80

Step1: Knock off a number from each side until you reach the center number(s)

71, 77, 77, 79, 79, 80, 88, 89, 91, 96 ---> 79, 80

Step 2: Find the mean(average) of the two central numbers

79 + 80 ---> 159 ÷ 2 = 79.5

Step 3: Round your answer

79.5 ---> 80

User Clemence
by
3.0k points
19 votes
19 votes

Answer:

Explanation:

Student A:

Mean 80.8

Median: 85.5

The Median is a higher score.

Student B:

Mean 82.7

Median: 79.5

Mean is a higher score

User Petiar
by
3.2k points