Question

The average of 11 numbers in a list is 14. If the average of 9 of the numbers in the list is 9, than what is the average of the other 2 numbers?

Answer 1

36.5

Answer 2

If 11 numbers has a mean of 14, then there must be a sum of 11*14=154. Now, if the first 9 have a mean of 11, then they would account for 9*11=99 of the necessary total of 154. Thus, the last two numbers have to make up the difference, i.e., the last two number must add up to 154-99=55. To get the mean of the last two numbers simply divide 5 by 2: \[55\div2=27.5\]

Answer 3

why 9*11?

Answer 4

Sorry, I mis-read; it should be 9*9=81. Then 154-81=73 followed by 73/2=36.5. Zarkon was correct.

Answer 5

thanks zarkon for the answer and thanks mandolino for explaining how to find it

Answer 6

\[\frac{x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}}{11}=14\]
\[x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11}=14(11)\]
\[x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9+x_{10}+x_{11} =154\]
\[\frac{x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9}{9}=9\]
*we don't really know which 9 but pretend its those 9
\[x_1+x_2+x_3+x_4+x_5+x_6+x_7+x_8+x_9=81\]
154-81=73

\[x_{10}+x_{11}=73 => \frac{x_{10}+x_{11}}{2}=\frac{73}{2}\]

Answer 7

now that is dedication :)

Answer 8

i did alot of copying and pasting lol