What is this formula measuring error?

Click For Summary
SUMMARY

The formula discussed, $$\frac{1}{\bar{x}}\sqrt{\frac{n\sum{x^2}-(\sum{x})^2}{n(n-1)}}$$, measures a type of error that exhibits poor behavior for data sets centered around zero. It scales differently than standard deviation or standard error as the sample size (N) increases. This inconsistency raises concerns regarding its applicability in statistical analysis. The Coefficient of Variation, referenced in the provided Wikipedia link, may offer additional insights into this formula's behavior.

PREREQUISITES
  • Understanding of variance and standard deviation
  • Familiarity with statistical error measures
  • Knowledge of sample size effects on statistical calculations
  • Basic proficiency in mathematical notation and formulas
NEXT STEPS
  • Research the Coefficient of Variation and its applications
  • Explore the derivation of the discussed formula
  • Learn about the limitations of error measures in statistics
  • Investigate alternative error metrics for datasets centered around zero
USEFUL FOR

Statisticians, data analysts, and researchers looking to deepen their understanding of error measurement in statistical analysis, particularly in relation to datasets with specific characteristics.

crashcat
Messages
46
Reaction score
33
TL;DR
I came across this formula that measures the distribution of measurements, but it makes no sense to me and I hope someone can explain it to me.
Variance and standard deviation and other measures of error I understand. This formula doesn't behave well for data sets centered around zero and also has other problems, like scaling differently as N increases than the standard deviation or standard error. Does anyone recognize this and can point me to a description or derivation? $$\frac{1}{\bar{x}}\sqrt{\frac{n\sum{x^2}-(\sum{x})^2}{n(n-1)}}$$
 
Physics news on Phys.org

Similar threads

High School Variance & Standard Deviation
  • · Replies 42 ·
2
Replies
42
Views
5K
Undergrad Error bars in Excel (standard deviation, standard error, percentage)
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Formula for the propagation of complex errors
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Error on the Mean: How to Compute w/ Individual Error
  • · Replies 37 ·
2
Replies
37
Views
6K
Undergrad How Is Uncertainty Calculated for the Mean of a Gaussian Function in MATLAB?
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Confused about error propagation
  • · Replies 22 ·
Replies
22
Views
2K
Graduate Confused about magnitude of error
  • · Replies 18 ·
Replies
18
Views
3K
Undergrad How Should I Calculate Error on the Mean with Identical Measurements?
  • · Replies 3 ·
Replies
3
Views
1K
Undergrad How to implement proper error estimation using MC
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Correctly Scaling the Standard Deviation for Scaled Measurements
  • · Replies 5 ·
Replies
5
Views
2K