What is the mean of all even integers from 123 to 987?

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.

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?

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.

To find the mean of all even integers from 123 to 987, follow these steps:

1. Determine the range of even integers from 123 to 987. Since the first even integer in this range is 124 (the next even number after 123), and the last even integer is 986 (the previous even number before 987), the range is from 124 to 986.

2. Find the average of the first and last terms in the range. In this case, the first term is 124 and the last term is 986. To find their average, simply add the two numbers together (124 + 986) and then divide the sum by 2.

Average = (124 + 986) / 2

3. Calculate the average:

Average = 1110 / 2

Average = 555

Therefore, the mean of all even integers from 123 to 987 is 555.