The following data represent a frequency distribution of 200 variables drawn fro

Question

The following data represent a frequency distribution of 200 variables drawn from a parent Gaussian population with mean ?=26.00 and standard deviation ?=5.00. The bins are two units wide and the lower edge of the first bin is at x=14.

4;8;11;20;26;31;29;22;26;13;5;2;3

Calculate "chi-squared" to test the agreement between the data and the theoretical curve.

what is the expectation value of "chi-squared"?

I've actually been provided the answers already to these questions [(chi-squared)=14.7 and <chi-squared>=V=N-1=12

I'm really not sure how to get the chi-squared of 14.7 (I have gotten close with 19, but obviously not using the right method). Any help would be appreciated.

Explanation / Answer

To determine the chi-square statistic, you take the difference of your data and the theoretical curve at each bin, square it and then sum those up.

In slightly more detail:

First calculate what your theoretical Gaussian value should be at each histogram bin center.

Then take the value of each real-data histogram bin, and find the difference.

Square each difference.

Sum those squares.

Then compare that value (your measured chi-square statistic) with the expected Chi-square value in your table. Hint the table's Chi-square is based on the number of degrees of freedom you have.

There is actually a bit of theory behind all of this, but ignoring all of that for now, that is what you want to do.

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