The mathematics SAT scores of the seven students in a mathem

The mathematics SAT scores of the seven students in a mathematics seminar are 538, 550, 570, 593, 610, 622, and 634. Suppose the student with the score 634 drops the seminar and is replaced by a student with a score of 600. What will happen to the mean and the median scores of the class?

A. Neither mean nor median will change.

B. The median will decrease, the mean will not change.

C. The median will not change, the mean will decrease.

D. Both mean and median will decrease.

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The number of vehicles passing through a pharmacy drive-up line with two windows during each 15-minute period was recorded. The results are shown below. Find the median number of vehicles going through the line in a fifteen-minute period.

16 8 24 22 30 19 18 27 11 15
17 24 26 23 7 25 21 16 20 14

A. 19.3

B. 20.1

C. 19.5

D. 19.6

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The federal government requires a car manufacturer to have a minimum miles per gallon (mpg) average over the models it makes. Suppose that the mpg’s for the five models of a manufacturer are 19, 21, 22, 28, and 18, and the government requirement is 27 mpg. The last of the models is to be redesigned to meet the government requirement. What must the new mpg of this model be to meet the requirement?

A. 27 mpg

B. 29 mpg

C. 30 mpg

D. 54 mpg

Solution

a) The median will not change; however the mean will decrease. This is because the median is the 4th place in this series, which remains unchanged with the value change, howvere, since the score of one of the scorer has decreased, hence this will lead to a reduced mean.

b) First we will have to arrange the series in the ascending order, which will come as:

7 8 11 14 15 16 16 17 18 19 20 21 22 23 24 24 25 26 27 30

Median = (n+1)/2 th term

Median = 10.5th term

For such cases, we take the average of the 10th and the 11th term.

Hence, Median = (19+20)/2 = 39/2 = 19.5

Median = 19.5

c) The average requirement of government is 27 mpg. So, the average of all 6 models should be 27mpg. Let the mpg for the latest model be X:

(19+21+22+28+18+X)/6 = 27

108+X = 27*6

108+X = 162

X = 162-108

X = 54

Hence, the mpg for the latest model should be 54mpg.