How can we find the variance of S_x, S_y, and S_z?

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In summary, the formula for finding the variance of S_x, S_y, and S_z is the sum of squared differences of each data point from the mean, divided by the total number of data points. The variance cannot be negative and decreases as the sample size increases. The standard deviation is the square root of the variance and is often used as a measure of variability. However, the variance cannot be used to compare data sets with different units as it is a measure of variability within a single data set and is not standardized.
  • #1
man@SUT
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Given |Psi> = a|up>+b|down>, in principle it should not be so difficult but when I calculate

Delta S=Sqrt[<S^2_x,S^2_y, or S^2_z>-<S_x,S_y, or S_z>^2]

the second term gives the problem. Lots of many terms a*, a, b*, b which is not canceled involve.

Whoever knows the way to get rid of this problem, please let me know.
 
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  • #2
Can you show what you've tried so far?
For example, how did you go about finding <S_x>?
 

1. What is the formula for finding the variance of S_x, S_y, and S_z?

The formula for finding variance is the sum of squared differences of each data point from the mean, divided by the total number of data points.

2. Can the variance of S_x, S_y, and S_z be negative?

No, the variance cannot be negative. It is always a non-negative value and indicates the spread or variability of the data.

3. How does the sample size affect the variance of S_x, S_y, and S_z?

The variance decreases as the sample size increases. This is because a larger sample size provides more accurate data and reduces the variability of the data.

4. What is the relationship between standard deviation and variance of S_x, S_y, and S_z?

The standard deviation is the square root of the variance. It measures the average distance of data points from the mean and is often used as a measure of variability.

5. Can the variance of S_x, S_y, and S_z be used to compare data sets with different units?

No, the variance cannot be used to compare data sets with different units. It is a measure of variability within a single data set and is not standardized, making comparisons between different data sets invalid.

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