Alyssa's test scores are listed below

Question

Alyssa's test scores are listed below

72, 87, 94, 80

Part A: Calculate the mean AND median of the given data. Show all your work. (1 points)

Part B: Alyssa just finished taking a fifth test. What score must she earn on her fifth test in order to have at least an 82% test average. Show all your work. (2 points)

Part C: How was the median affected by the addition of the fifth test score? (1 point)

Answer 1

Part A: To find the mean, we add up all the scores and divide by the total number of scores:

72 + 87 + 94 + 80 = 333
333 ÷ 4 = 83.25

So the mean score is 83.25.

To find the median, we need to put the scores in order from least to greatest:

72, 80, 87, 94

Since there are an even number of scores, the median is the average of the middle two scores:

(80 + 87) ÷ 2 = 83.5

So the median score is 83.5.

Part B: To find out what score Alyssa needs on her fifth test, we need to use the formula for finding a weighted average:

average = (sum of weights × corresponding values) ÷ total weight

Since Alyssa has already taken four tests, her total weight is 4. To get an average of 82%, we can set up an equation:

0.82 = (4 × average so far + 1 × score on fifth test) ÷ 5

We can plug in the values we know:

0.82 = (4 × 83.25 + score on fifth test) ÷ 5

To solve for the score on the fifth test, we can multiply both sides by 5 and then subtract 4 times the average so far:

0.82 × 5 = 4 × 83.25 + score on fifth test
4.1 = 333 + score on fifth test
score on fifth test = 4.1 - 333
score on fifth test = -328.9

Obviously, a score of -328.9 is not possible, so Alyssa cannot get an average of at least 82% with her current scores. She will need to get a higher score on her fifth test.

Part C: The median is not affected by the addition of the fifth test score unless the fifth test score is one of the middle two scores (in this case, 80 and 87). If the fifth test score is higher than 87, then the median will increase. If the fifth test score is lower than 80, then the median will decrease. If the fifth test score is between 80 and 87, then the median will stay the same.