Question 1045782: A group of patients is recruited for a clinical trial. Their heights, recorded in centimeters are:
184, 176, 181, 157, 168, 154, 148, 165, 190, 162.
Two more patients are recruited to the study. After these patients join, the mean height is 169 cm. which of the following could be the heights of the two new patients?
A) 146 cm and 177 cm
B) 150 cm and 188 cm
C) 165 cm and 177 cm
D) 157 cm and 186 cm
I found the mean of the 10 patients as 168.5 cm but I don't know what to do after
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! you've got 10 patients.
their heights are 184, 176, 181, 157, 168, 154, 148, 165, 190, 162.
the sum of their heights is 1685.
average is equal to sum divided by number of patients.
sum is equal to average times number of patients.
average is therefore equal to 1685 / 10 = 168.5
this agrees with the average you posted.
you are adding 2 new patients.
after those patients are added, the average is 169.
since sum equals average * number of patients, then the sum of the 12 patients should be 12 * 169 = 2028.
your new total is 2028 with 12 patients.
your previous total is 1685 with 10 patients.
the difference is 2028 - 1685 = 343 with 2 patients.
look for pairs of numbers that add up to 343.
that looks like selection D.
selection D is:
D) 157 cm and 186 cm
add them together and you get 343.
add 343 to 1685 and you get 2028.
divide 2028 by 12 and you get an average of 169.
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