Question

the first 9 players named to the all - star basketball team have scored a mean (average) of 22.0 points per game, as shown below
all - star player
points per game scoring
mark 20.0
jay 21.5
evan 22.0
norm 25.0
shawn 18.0
tim 16.5
brian 28.0
lee 27.0
zeke 20.0
which two players could be added to the all - star team without changing the average points per game scored by players on the team?
a adam (16.0) and herb (26.0)
b mike (20.0) and greg (22.0)
c sam (13.0) and manny (31.0)
d paul (18.0) and dan (24.0)

Explanation:

Step1: Calculate the total points of the first 9 players

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Given \(n = 9\) and \(\bar{x}=22\), then \(\sum_{i=1}^{9}x_{i}=n\times\bar{x}=9\times22 = 198\)

Step2: For each option, calculate the new total and new mean

• Option A:

New total \(=198+16 + 26=240\), new \(n=9 + 2=11\), new mean \(\frac{240}{11}\approx21.82\)

• Option B:

New total \(=198+20+22 = 240\), new \(n = 9+2=11\), new mean \(\frac{240}{11}\approx21.82\)

• Option C:

New total \(=198+13+31=242\), new \(n=9 + 2=11\), new mean \(\frac{242}{11}=22\)

• Option D:

New total \(=198+18+24=240\), new \(n=9+2=11\), new mean \(\frac{240}{11}\approx21.82\)

Answer:

C. Sam (13.0) and Manny (31.0)