Question

The mean of 11 numbers is 49. Removing one of the numbers causes the mean to decrease to 45. What number was removed?

Answer 1

Explanation:

(x1 + x2 + ... + x11)/11 = 49

x1 + x2 + ... + x11= 49×11 = 539

(x1 + x2 + ... + x10)/10 = 45

x1 + x2 + ... + x10 = 45×10 = 450

so, the difference in both sums is

539 - 450 = 89

89 was the removed number.

Answer 2

89

Explanation:

The mean:

`\overline{x}=(a_1+a_2+a_3+...+a_n)/(n)`

We have:

`\overline{x}=49;\ n=11`

Then we have

`(11\cdot49)/(11)=49`

`n` - the number

new mean is equal 45.

Therefore we have the equation:

`(11\cdot49-n)/(11-1)=45\\\\(539-n)/(10)=45\qquad|\text{multiply both sides by 10}\\\\539-n=450\qquad|\text{subtact 539 from both sides}\\\\-n=-89\qquad|\text{change the signs}\\\\n=89`