Question

Suppose your Unit Quiz grades have been: 85%, 80%, 96%, 72%, 78%, 85% and 92%

a) What is your average/mean score?

b) What is the median score?

c) What is the mode score?

d) Why is the mean lower than the median?

e) What will your mean be if you get a perfect score of 100% on your next quiz?

Answer 1

The average/mean score is 56. The median score is 85. There is no mode score. The mean is lower than the median because of the influence of extreme values. The mean with a perfect score of 100% in the next quiz will be 82.25.

Step-by-step explanation:

a) To calculate the average/mean score, add up all the quiz grades and divide by the number of quizzes. For this set of grades, the average is (85 + 80 + 96 + 72 + 78 + 85 + 92) / 7 = 392 / 7 = 56.

b) To find the median score, arrange the grades in ascending order and find the middle value. In this case, the median is 85.

c) The mode is the score that appears most frequently. Since there are no scores that repeat, there is no mode.

d) The mean is lower than the median because the mean is influenced by extreme values, while the median is not. In this case, the lower scores of 72 and 78 pull down the mean.

e) If you get a perfect score of 100% on your next quiz, your new mean will be (85 + 80 + 96 + 72 + 78 + 85 + 92 + 100) / 8 = 658 / 8 = 82.25.

Answer 2

mean: 84

median: 85

mode: 85

explainations for d and e below.

Step-by-step explanation:

mean:

(85+80+96+72+78+85+92)/7 = 544/7 = 84

median:

sort them in order from least to greatest first

72, 78, 80, 85, 85, 92, 96

find the middle number in that order, that's your median. in this case, it's 85.

mode:

number that appears the most in the order; the frequency. in this case as well, it's also 85.

answer for d:

the reason why the mean is lower than the median is because of the fact we were figuring out the average and had to divide, unlike the median where it's just the middle of the order we have.

answer for e:

(85+80+96+72+78+85+92+100)/8 = 644/8 = 80.5%

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