consider the numbers in pairs, from the ends in:
124 ... 554 556 ... 986
Each pair has an average of 555, so the whole string of numbers has that same average.
What is the mean of all even integers from 123 to 987?
3 answers
let's do a little experiment:
find the mean or average of all the even numbers form 4 to 12
(4+6+8+10+12)/5
= 8
mmmh, isn't that the middle number ?
and isn't the middle number (4+12)/2 ????
mmmmhhh?
find the mean or average of all the even numbers form 4 to 12
(4+6+8+10+12)/5
= 8
mmmh, isn't that the middle number ?
and isn't the middle number (4+12)/2 ????
mmmmhhh?
However, if you want an algebraic solution, rather than a feel-good one, consider the numbers as a arithmetic progression with
a = 124
d = 2
n = (986-124)/2 + 1 = 432 terms
Sum = 432/2 (124+986) so, the average
Avg = Sum/432 = 1/2 (124+986) = 555
as we posited above.
a = 124
d = 2
n = (986-124)/2 + 1 = 432 terms
Sum = 432/2 (124+986) so, the average
Avg = Sum/432 = 1/2 (124+986) = 555
as we posited above.