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# 10. There are 3 statistics teachers in the classroom. Their ages are 30, 40, and 50. A 39-year-old statistics teacher enters the classroom.

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10. There are 3 statistics teachers in the classroom. Their ages are 30, 40, and 50. A 39-year-old statistics teacher enters the classroom. Explain your thinking.

A. The mean age will increase and variance will decrease.

B. The mean age will stay the same and variance will decrease.

C. The mean age and variance will decrease.

D. The mean age and variance will increase.

E. The mean age will decrease and variance will increase.

11. A 5-number summary for scores on an APCS exam is 71, 75, 81, 90, 99. Assume 36 students took the test, about how many had scored between 90 and 99? Explain your thinking.

A. 18

B. 36

C. 9

D. 75

E. 27

Nov 12, 2020

#1
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Hey, GM......good to see you  !!!

Here's  the first one

Mean  age of the first  3 teachers   =  (30 + 40 + 50)/3 =  40

Mean age  of 4 teachers ( 30 + 40 + 50 + 39) / 4  = 39.75

Variance of  three teachers

[(50  - 40)^2  + (40 -40)^2  + (30 -40)^2 ]  =  [10^2  + 0  + (-10)^2]    = 200

Variance  with 4th teacher

[ (50 - 39.75)^2  + (40 -39.75)^2  + (39 - 39.75)^2  + (30 - 39.75)^2 ]   =

[ 10.25^2  + .25^2  + (-.75)^2  + ( -9.75)^2  ]  = 200.75

So.....the mean  decreases and  variance  increases

Nov 12, 2020
#2
+1063
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Thank you so much CPhill! I'm so glad to see you again here. It has been so long since I last saw you and I thought something happened because you weren't on the leaderboards.

GAMEMASTERX40  Nov 12, 2020
#3
+112105
+1

I just took a lengthy break.....I'm still hanging in here  ...LOL!!!!

CPhill  Nov 12, 2020