Calculating variance from range

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SUMMARY

The discussion centers on calculating variance from a given range of sample data. The user has five samples with an average concentration of 5 mg and a range of 0.003 mg. It is established that variance cannot be directly calculated from the range alone; however, it can be estimated using the five sample data points. The method involves summing the squares of the differences between each sample point and the average, then dividing by 4 (n-1) to obtain an unbiased estimate of the variance.

PREREQUISITES
  • Understanding of basic statistical concepts, including variance and standard deviation.
  • Familiarity with sample data and how to calculate averages.
  • Knowledge of the formula for calculating variance from sample data.
  • Basic proficiency in statistical analysis tools or software.
NEXT STEPS
  • Learn how to calculate variance using sample data in Python with libraries like NumPy.
  • Study the properties of different statistical distributions to understand variance estimation.
  • Explore the concept of unbiased estimators in statistics.
  • Investigate the relationship between standard deviation and variance in depth.
USEFUL FOR

Statisticians, data analysts, and anyone involved in statistical data analysis who needs to estimate variance from limited sample information.

Dawei
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Hello,

I have taken 5 samples and found that my average concentration is 5 mg, with a range of .003 mg in either direction. I would like to calculate the variance with only this information.

Is this possible? I am used to calculating the variance from the standard deviation, but I don't have this available.
 
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No, it's not possible. But if you know about the shape of the distribution you may be able to estimate the variance.
 
You can use the 5 sample data points to estimate the variance. Take the sum of the squares of the differences between the individual points and the average. Then divide by 4 (n-1 in general). This is an unbiased estimate for the variance.
 

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