Question

HI PLEASE HELP ON QUESTION ASAP I ALREADY KNOW ANSWER =75

BUT how do i work it out in an exam so exam marker knows what your doing



2)the mean of 6 numbers is 25. If one of the remaining numbers is removed, the average of the remaining numbers is 15. What is the number that was removed?

Answer 1

The number that was removed was 75

Look in explanation for working out how you get this

Explanation:

mean1 = 25

if one is removed, we get mean2 = 15

now, mean1 is mean of 6 numbers, so,

`mean1 = (n1+n2+n3+n4+n5+n6)/6`

so,

`(mean1)(6) = (n1+n2+n3+n4+n5+n6) \ \ \ (I)`

where "n" means number

now, we removed a number, let that number be n6,

so, after we remove it, we get the 2nd mean,

`mean2 = (n1+n2+n3+n4+n5)/5\\\\and,\\(5)(mean2) = (n1+n2+n3+n4+n5)`

so, n1 + n2 +n3+n4+n5 = (5)(mean2)

putting the value of n1 + n2 +n3+n4+n5

in eq (I), we get,

`(mean1)(6) = (5)(mean2)+n6 \ \ \`

so, we know the values of mean1 =25 and mean2 = 15

we get,

`(6)(25)=(5)(15) = n6\\n6 = (25)(6)-(15)(5)\\n6=150-75\\n6=75`

Hence the number that was removed was 75