Doug had scores of 80, 85, 75, and 80 on his first four

exams in a course.
a. Find the mean, median, and mode for these exam
scores.
b. Which “average” would Doug want the teacher to use
in determining his grade?
c. What score would Doug have to get on a fifth examination
to raise his mean score to 84? Is it reasonable
to expect Doug to achieve that score?

http://edhelper.com/statistics.htm

I get the mode , mean and median are all 80. right?

To find the mean, median, and mode for Doug's exam scores, let's go through the steps:

a. Mean: The mean is the average of the scores. To find the mean, add up all the scores and then divide by the total number of scores.

80 + 85 + 75 + 80 = 320

320 ÷ 4 = 80

The mean of Doug's exam scores is 80.

Median: The median is the middle value of the scores when they are arranged in ascending order. In this case, since Doug has four scores, the middle two scores will be averaged to find the median.

Arranging the scores in ascending order: 75, 80, 80, 85

Taking the average of the middle two scores: (80 + 80) ÷ 2 = 80

So, the median of Doug's exam scores is 80.

Mode: The mode is the score that appears most frequently. In this case, there is no repeating score, so there is no mode for Doug's exam scores.

b. The most favorable "average" for Doug would be the highest one. In this case, the median and mean are both 80, so he wouldn't have a preference between those two. However, since there is no mode, it doesn't play a role in determining his grade.

c. To raise the mean score to 84, we need to find the total sum of the scores for all 5 exams.

Current total sum: 80 + 85 + 75 + 80 = 320

To find the fifth score, we can use the formula:

Sum of all 5 scores = (Mean score) * (Total number of scores)

Substituting the values we know:

(84) * (5) = 420

To find the fifth score, subtract the current sum from the desired sum:

420 - 320 = 100

Doug would need to get a score of 100 on the fifth examination to raise his mean score to 84. However, achieving a perfect score of 100 might be challenging, so it may or may not be reasonable to expect Doug to achieve that score.