Figure out summation(x^2) in summation equation[Simple]

In summary, the conversation discusses a problem involving finding the mean and estimated variance for a sample of flour bags. The given information includes a sum of (x-500) and (x-500)^2, and the goal is to find the sum of x^2. After solving for the sum of x^2, the solution is found to be 34735178.
  • #1
giddy
28
0
Hi,
So this is just part of my problem but its got me stumped for days and I can't ignore it since its popping up too often in my problems.

Homework Statement


For A sample of 140 bags of flour. The masses of x grams of the contents are summarized by [tex]\sum (x - 500) = -266[/tex] and [tex] \sum (x-500)^2=1178[/tex] I need to find the mean and estimated variance. The mean is simple 140(x - 500) = -266; mean = 498.3 But how the heck do I figure out [tex]\sum x^2[/tex] with the above info? I need only [tex]\sum x^2[/tex]

The Attempt at a Solution


Mostly I just doodled pages trying to get this one! =S I tried [tex]140(x - 500)^2 = 1178[/tex] And solve it, comes out as x = -1.780 or - 998.22. Which isn't correct. I need [tex]\sum x^2[/tex] basically in the formula for estimated variance [tex]s^2 = \frac{1}{n-1}(\sum x^2 - \frac{(\sum x)^2}{n})[/tex]
I tried reworking from the answer(variance=4.839) so sum of x2 should be 34773692.21 but I don't know how to get to this answer?
 
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  • #2
You have a sum(x_squared) in your second equation if you expand it. Just like you have a sum of x in your first.
 
  • #3
Sorry I am not sure what you mean =S

If I do expand (x - 500)^2 it'll be x^2 - 2(500)(x) + 500^2 Right? So where would I get sum of x? How would I expand sum(x^2)
 
  • #4
giddy said:
How would I expand sum(x^2)

You don't have to expand it, just solve for it.
 
  • #5
You have
[tex]\sum_{i = 1}^{140}(x_i - 500)^2 = 1178[/tex]
You can expand the sum on the left, and solve for [itex]\sum x^2[/itex].

[tex]\sum_{i = 1}^{140}(x_i - 500)^2 = 1178[/tex]
[tex]\Rightarrow \sum_{i = 1}^{140}x_i^2 -2\sum_{i = 1}^{140} 500*x_i + \sum_{i = 1}^{140}500^2 = 1178[/tex]
The second and third summations on the left can be simplified and substituted for.
 
  • #6
aha.. ok so i didn't even know how to really solve summation equations, but I looked it up.

So Sum(x^2) = 34735178! And its correct... =)
 

1. What is summation and how is it used in scientific calculations?

Summation is a mathematical operation that adds together a series of numbers or terms. It is commonly used in scientific calculations to represent the total value of a set of data.

2. How do I express summation in an equation?

Summation is often expressed using the Greek letter sigma (Σ) followed by the terms to be added. The starting and ending points of the summation are written below and above the sigma symbol, respectively. For example, Σ(x^2) would represent the summation of all terms of x^2 from the starting point to the ending point.

3. What is the summation equation for x^2?

The summation equation for x^2 would be Σ(x^2), where x^2 is the term being added and the summation is performed from the starting point to the ending point.

4. How is summation used to find the total value of a set of data?

Summation is used to find the total value of a set of data by adding together all the individual values or terms. It is often used in statistical analysis to calculate the mean, or average, of a data set.

5. Can summation be used for more complex calculations?

Yes, summation can be used for more complex calculations by including additional operations within the summation, such as multiplication, division, and exponentiation. It can also be used with multiple variables and nested summations to represent more complex mathematical relationships.

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