1. ## A general question about mean

some times while finding mean (average) just taking out the average of the first and the last number helps, but sometimes i have to find out the sum of all the numbers, even after arranging in ascending order. plzz clear my confusion.

2. Originally Posted by saha.subham
some times while finding mean (average) just taking out the average of the first and the last number helps, but sometimes i have to find out the sum of all the numbers, even after arranging in ascending order. plzz clear my confusion.

Average of $10,11,12,13,14,15,16$ is 13, you can obtain this by adding those numbers and dividing by 7, which is how many numbers you add up

The above method always works for any set of numbers.

Note you can also do $\frac{10+16}{2}=13$

Now the average of 2,4,6,8 is 5. You can add them up and divide by 4, or you can average the first and last numbers.

If you write them in a different order, you can no longer average the first and last numbers, you have to average the smallest and largest number.

This only works is the above 2 situations because the difference between all of the numbers is the same. 10+1=11, 11+1=12.... 15+1=16 so the difference in the first is 1, and in the second it is 2.

Consider 1,3,95. The average of these is 33 but you cannot average the first and last to get this because the difference between 1 and 3 is 2, but the difference between 95 and 3 is 92.