Estimate mean and std dev?

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April 8th 2009, 11:50 AM
rba_mandy

Estimate mean and std dev?

A random sample of 13 observations from a population yielded $\sum$ x=488.8 and $\sum$ $x^2$ = 18950.2. Estimate $\mu$ and $\sigma.$

I can't find this in my notes, I think $\sum$ x = 488.8 would be the sum of the sample, not sure where to go from there.

Thank you
April 8th 2009, 02:37 PM
mr fantastic

Quote:

Originally Posted by rba_mandy

A random sample of 13 observations from a population yielded $\sum$ x=488.8 and $\sum$ $x^2$ = 18950.2. Estimate $\mu$ and $\sigma.$

I can't find this in my notes, I think $\sum$ x = 488.8 would be the sum of the sample, not sure where to go from there.

Thank you

$\overline{x} = E(X) = \frac{\sum_{i=1}^n x_i}{n}$

$s_X^2 = Var(X) = \frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n} = \frac{\left(\sum_{i=1}^n x_i^2\right) - 2 \overline{x} \left( \sum_{i=1}^n x_i \right) + n \overline{x}^2}{n}$ .

$= \frac{\sum_{i=1}^n x_i^2}{n} - 2 \overline{x} \frac{\sum_{i=1}^n x_i}{n} + \overline{x}^2$

$= \frac{\sum_{i=1}^n x_i^2}{n} - \overline{x}^2$ .

Substitute your data and do the calculations.
April 8th 2009, 03:47 PM
rba_mandy

Quote:

Originally Posted by mr fantastic

$\overline{x} = E(X) = \frac{\sum_{i=1}^n x_i}{n}$

$s_X^2 = Var(X) = \frac{\sum_{i=1}^n (x_i - \overline{x})^2}{n} = \frac{\left(\sum_{i=1}^n x_i^2\right) - 2 \overline{x} \left( \sum_{i=1}^n x_i \right) + n \overline{x}^2}{n}$ .

$= \frac{\sum_{i=1}^n x_i^2}{n} - 2 \overline{x} \frac{\sum_{i=1}^n x_i}{n} + \overline{x}^2$

$= \frac{\sum_{i=1}^n x_i^2}{n} - \overline{x}^2$ .

Substitute your data and do the calculations.

Ok, but I don't understand these formulas. What is $\frac{\sum_{i=1}^n x_i}{n}$ the n over i?

Is the first formula for $\mu$ and the second for $\sigma$ ?

Could you possibly give me a head start or an example maybe?

Thanks for your help.
April 9th 2009, 02:43 AM
mr fantastic

Quote:

Originally Posted by rba_mandy

Ok, but I don't understand these formulas. What is $\frac{\sum_{i=1}^n x_i}{n}$ the n over i?

Is the first formula for $\mu$ and the second for $\sigma$ ?

Could you possibly give me a head start or an example maybe?

Thanks for your help.

$\sum_{i=1}^n x_i$ is the sum of all the data.

$\sum_{i=1}^n x_i^2$ is the sum of the squares of all the data.

$n$ is the number of data points.

You have been given the value of these three things. Substitute them into the formulae I gave you.
April 9th 2009, 11:56 AM
rba_mandy

Ok, I think I understand. Thank you for the help. (Happy)