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?
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A. The mean 80+85+75+80=320
320/4=80
Median is 80: 75, 80, 80 ,85
0,0,5,7,8,8,8 mode is 8
B. 80
C. 84 x 5= 420-320=100. Doug would have to make a 100% to have an average of 84. No it isn’t reasonable for
Doug to score 100.
Your median and mean are correct. The mode is also 80.
Your other answers are correct.
Sweet! Thanks
You're welcome.
a. To find the mean, add up all the exam scores and divide by the number of exams:
Mean = (80 + 85 + 75 + 80) / 4 = 320 / 4 = 80
To find the median, arrange the exam scores in ascending order and find the middle value:
Arranged scores: 75, 80, 80, 85
Median = (80 + 80) / 2 = 160 / 2 = 80
The mode is the value that appears most frequently. In this case, there is no mode since all the scores appear only once.
b. In determining Doug's grade, he would want the teacher to use either the mean or the median. Since both the mean and the median are 80 in this case, it doesn't matter which one is used.
c. Let's calculate the current total points Doug has earned:
Total points = (80 + 85 + 75 + 80) = 320
To find the score Doug needs to raise his mean to 84, we can set up the following equation:
(320 + x) / 5 = 84
Multiplying both sides by 5 to get rid of the fraction:
320 + x = 420
Subtracting 320 from both sides to isolate x:
x = 420 - 320
x = 100
Doug would need to score 100 on his fifth examination to raise his mean score to 84. Whether it is reasonable to expect Doug to achieve that score depends on his previous performance and his ability to improve. Without more information, it's difficult to determine if it's reasonable or not.