Calculating Overall Variance & Standard Deviation for 3 Sets of Data

In summary, the conversation is about calculating the overall variance and standard deviation for three sets of resonators. If the resonators are independent, the overall variance can be calculated by adding the variances of each set. However, if they are not independent, the overall variance calculation also includes the covariance between the sets. The last term in the equation may be a typo and should possibly be Cov(X_1,X_3). Additionally, it is noted that if there are an infinite number of sets, the overall variance and standard deviation will also be infinite.
  • #1
Excom
61
0
Hi

If I have measured the resonance frequency of three sets of resonators and calculated the mean, variance and standard deviation for each set. How do I add the three variances and standard deviations to get an overall variance and standard deviation?

Well, I know that the standard deviation is the square root of the variance and therefore I only need to know how to calculate the overall variance.

I hope that someone can help me with my problem. Thanks in advance.

Best regards
Tom
 
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  • #2
If your three resonance frequencies are independent, then

[tex]Var(X_1+X_2+X_3)=Var(X_1)+Var(X_2)+Var(X_3)[/tex]

If not, then

[tex]Var(X_1+X_2+X_3)=Var(X_1)+Var(X_2)+Var(X_3)+2Cov(X_1,X_2)+2Cos(X_2,X_3)+2Cov(X_1,X_2)[/tex]
 
  • #3
micromass said:
If your three resonance frequencies are independent, then

[tex]Var(X_1+X_2+X_3)=Var(X_1)+Var(X_2)+Var(X_3)[/tex]

If not, then

[tex]Var(X_1+X_2+X_3)=Var(X_1)+Var(X_2)+Var(X_3)+2Cov(X_1,X_2)+2Cos(X_2,X_3)+2Cov(X_1,X_2)[/tex]

Is your last term meant to be Cov(X_1,X_3)?
 
  • #4
Thanks

One clarifying question. If I have an infinite number of sets and I then add the variances for all the sets then the variance and hence the standard deviation will also be infinite?
 
  • #5


Hello Tom,

To calculate the overall variance and standard deviation for three sets of data, you will need to use the formula for pooled variance. This formula takes into account the individual variances and sample sizes of each set of data.

The formula for pooled variance is:

s^2p = ((n1-1)s1^2 + (n2-1)s2^2 + (n3-1)s3^2) / (n1 + n2 + n3 - 3)

Where:
s^2p = pooled variance
n1, n2, n3 = sample sizes for each set of data
s1, s2, s3 = individual variances for each set of data

To calculate the overall standard deviation, simply take the square root of the overall variance.

I hope this helps and good luck with your calculations!

Best regards,
 

FAQ: Calculating Overall Variance & Standard Deviation for 3 Sets of Data

1. What is the purpose of calculating overall variance and standard deviation for 3 sets of data?

The purpose of calculating overall variance and standard deviation for 3 sets of data is to measure the amount of variability or spread in the data. This allows for a better understanding of the data and can help identify any patterns or trends.

2. How do you calculate the overall variance for 3 sets of data?

The overall variance for 3 sets of data can be calculated by finding the variance for each set of data and taking the average of these variances. The formula for variance is (sum of squared differences from the mean) / (number of data points - 1).

3. What does the standard deviation represent in this calculation?

The standard deviation represents the average amount of deviation or variability from the mean. It is a measure of how spread out the data is and is calculated by taking the square root of the variance.

4. Why is it important to calculate the overall variance and standard deviation for 3 sets of data?

Calculating the overall variance and standard deviation for 3 sets of data is important because it provides a comprehensive understanding of the data. It can help identify any outliers or unusual patterns, as well as compare the variability between the different sets of data.

5. Are there any limitations to using variance and standard deviation to analyze data?

Yes, there are limitations to using variance and standard deviation to analyze data. These measures are sensitive to outliers and may not accurately represent the data if there are extreme values. Additionally, they only provide information about the spread of the data and do not take into account the shape or distribution of the data.

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