Calculating Average Wave Speed and Standard Error

[neoking77]

[SOLVED] Standard error

Homework Statement

A student determined the following values for the wave speed; calculate the average value of the wave speed and its standard error

50.8, 50.6, 51.8, 52.0, 50.9, 51.6, 51.3, 51.5

Homework Equations

avg wave speed = 51.3

The Attempt at a Solution

how do i get the standard error? the answer is (51.3+/-0.2)
i am aware that Se = standard deviation / sqrt(number of data)
but I'm not sure how to get standard deviation.

any help would be greatly appreciated, thank you.

 

[danago]

Standard deviation is given by:

$$\sigma = \sqrt {\frac{1}{n}\sum\limits_{i = 0}^n {(x_i - \overline x )^2 } }$$

So what you can do is find the difference between each of the scores and the mean (which you calculated as 51.3) and then square those differences, and then add them all. Finally, divide it by the number of scores you have, and find the square root of it all.

 

[danago]

Another form of the standard deviation equation is:
$$\sigma = \sqrt {\frac{1}{n}\sum\limits_{i = 0}^n {x_i ^2 - \overline x ^2 } }$$

So another way is to add the squares of each score, then divide it by the total number of scores, then subtract the square of the mean, and then square root it all.

 

[neoking77]

thank you very much!