Question about what this variance value means

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The calculated variance of 3.65 indicates the degree of dispersion in the dataset. For a normal distribution, approximately 69% of the values fall within +/- 3.65 units of the mean. However, it is clarified that typically, 68-69% of values are within one standard deviation of the mean, which corresponds to the square root of the variance. Variance represents the average of the squared distances from the mean, similar to standard deviation, which also measures data spread. Understanding these concepts is crucial for accurate data analysis.
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i calculated the variance of a few measurements and i got the value of 3.65

i know the variance tells us the degree of dispersion from them ean value, and i came up with 3.65, what does this number say about the data?
 
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If you're dealing with a normal distribution, it tells you that about 69% of your values are within +/- 3.65 units of the mean.
 
Mark44 said:
If you're dealing with a normal distribution, it tells you that about 69% of your values are within +/- 3.65 units of the mean.

thank you
 
Mark44 said:
If you're dealing with a normal distribution, it tells you that about 69% of your values are within +/- 3.65 units of the mean.

I thought that in a normal distribution, 69% of your values are within +/- one standard deviation of the mean. So in this case, 68-69% of the data will be in the interval between \mu - \sqrt{3.65} and \mu + \sqrt{3.65}, if your mean is \mu.

Variance is the average of the squares of the distance between your data and the mean. Like standard deviation, it also measures how spread out your data is.
 
mathie.girl said:
I thought that in a normal distribution, 69% of your values are within +/- one standard deviation of the mean. So in this case, 68-69% of the data will be in the interval between \mu - \sqrt{3.65} and \mu + \sqrt{3.65}, if your mean is \mu.

Variance is the average of the squares of the distance between your data and the mean. Like standard deviation, it also measures how spread out your data is.
Thanks for the correction. The (population) variance is the square of the (population) standard deviation.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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