Question

chapter 2 homework assignment
score: 10/76 answered: 3/12
question 4
1.44 make - up exam: in a class of 22 students, 21 of them took an exam in class and 1 student took a make - up exam the following day. the professor graded the first batch of 21 exams and found an average score of 84 points with a standard deviation of 7.5 points. the student who took the make - up the following day scored 63 points on the exam.
a) does the new students score increase or decrease the average?
increases
decreases
b) the new average is: (round to two decimal places)
c) does the new students score increase or decrease the standard deviation of the scores?
increases
decreases

Explanation:

Step1: Compare make - up score and original average

The original average of 21 students is 84 points and the make - up student scored 63 points. Since 63 < 84, the new student's score will decrease the average.

Step2: Calculate the new average

The sum of the scores of the first 21 students is $21\times84 = 1764$ points. The sum of scores of all 22 students is $1764+63=1827$ points. The new average is $\frac{1827}{22}\approx83.05$ points.

Step3: Analyze the effect on standard deviation

The standard deviation measures the spread of data from the mean. The original mean was 84 and the new data point (63) is further from the new mean (83.05) compared to most of the original 21 data - points from the original mean of 84. So the standard deviation will increase.

Answer:

a) Decreases
b) 83.05
c) Increases