Math Help - Summation notation

1. Summation notation

If I had 12 measurements: 30, -38, -70, -78, 32, 73, 49, -88, 29, 32, 42, 6, and they were labeled x1, x2, x3 etc, how would I find the following?

Find .

I added all the numbers, and came up w/19. Then I took x1 which was 30 and added 49 to that and then multiplied that by 19 and came up w/1501 which is the wrong answer. Can anybody help me w/this? Thank you.

2. Originally Posted by Y-rag
If I had 12 measurements: 30, -38, -70, -78, 32, 73, 49, -88, 29, 32, 42, 6, and they were labeled x1, x2, x3 etc, how would I find the following?

Find .

I added all the numbers, and came up w/19. Then I took x1 which was 30 and added 49 to that and then multiplied that by 19 and came up w/1501 which is the wrong answer. Can anybody help me w/this? Thank you.

Would this be 19+49= 68? Would that be the answer?

3. $\sum_{i=1}^{12}(x_i+49)=\sum_{i=1}^{12}x_i+\sum_{i =1}^{12}49$

Now since $\sum_{i=1}^{12}49=49(12)$

and

$\sum_{i=1}^{12}x_i=30+(-38)+(-70)+(-78)+32+73+49+(-88)+29+32+42+6$

we have

$\sum_{i=1}^{12}(x_i+49)=30+(-38)+(-70)+(-78)+32+73+49+(-88)+29+32+42+6+[12(49)]

$

Can you handle it from here buddy?

4. VonNemo, I get 607. Does that seem like I handled it?

This is worse than learning to play the piano and I've never done that but I can guess how painful it would be.

5. I'm getting 607. Try again. Always check your work, man.

6. I corrected myself after I sent the wrong number, I got 607 also. Dumb mistake on my part. Thank you immensely.