help

I agree with the answers given (-5), but I don't understand their methods.

To find the mean, you need to add all the numbers together and then divide by the number of numbers.

Adding all the numbers:  -410 + -409 + -408 + ... + -2 + -1 + 0 + 1 + 2 + ... + 398 + 399 + 400

gives you -410 + -409 + -408 + -407 + -406 + -405 + -404 + -403 + -402  +  -401  =  -4055.

(I agree with Anonymoushq that the number below 0 (-400, - 399, ... -2, -1) cancel those above 0 (1, 2, ..., 399, 400).)

Having the sum (-4055), you need to divide by the number of numbers, which is 811; there are 410 numbers below 0, then 0, then 400 numbers above 0, giving yous 410 + 1 + 400  =  811 numbers.

Mean  =  Sum / Number of Numbers  =  -4055 / 811  =  -5.

-410 + 400=-10

-10/2=-5 is the mean.

The answer is -5 

because you can cancel out both 400 hundreds because they are the same, so you are at zero you and then faced with -10 and 0 so in the middle is -5.

hope this helps :)

geno wrote; "I agree with the answers given (-5), but I don't understand their methods." 

I, too, was puzzled at first.  I wondered if it was a coincidence due to the choice of numbers used or if it was more generally true.  A little analysis shows it is generally true - see below:

.