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Variance

Variance

The deviations show how spread out the data are about the mean. A positive deviation occurs when the data value exceeds the mean, whereas a negative deviation occurs when the data value is less than the mean. If the deviations are added, the sum is always zero. So one cannot simply add the deviations to get the data spread. By squaring the deviations, the numbers are made positive; thus, their sum will also be positive.The standard deviation measures the spread in the same units as the data.

Standard Deviation

Standard Deviation

The most commonly used measure of variation is the standard deviation. It is a numerical value measuring how far data values are from their mean. The standard deviation value is small when the data are concentrated close to the mean, exhibiting slight variation or spread. The standard deviation value is never negative, it is either positive or zero. The standard deviation is larger when the data values are more spread out from the mean, which means the data values are exhibiting more...

Testing a Claim about Standard Deviation

Testing a Claim about Standard Deviation

A complete procedure to test a claim about population standard deviation or population variance is explained here.
The hypothesis testing for the claim of population standard deviation (or variance) requires the data and samples to be random and unbiased. The population distribution also must be normal. There is no specific requirement on the sample size as the estimation is based on the chi-square distribution.
As a first step, the hypothesis (null and alternative) concerning the claim about...

Contaminants and Errors

Contaminants and Errors

Effective sample preparation is crucial for accurate and reliable laboratory analysis. During this process, two significant sources of error can arise: concentration bias from improper sample splitting and contamination caused by methods used to reduce particle size, such as grinding or homogenization. Identifying and minimizing these potential errors is crucial to ensuring the validity of the analysis.
Another key consideration is determining the appropriate number of samples required to...

Range Rule of Thumb to Interpret Standard Deviation

Range Rule of Thumb to Interpret Standard Deviation

The range rule of thumb in statistics helps us calculate a dataset's minimum and maximum values with known standard deviation. This rule is based on the concept that 95% of all values in a dataset lie within two standard deviations from the mean.
For instance, the range rule of thumb can be used to find the tallest and the shortest student in a class, given the mean student height and standard deviation. If the mean student height is 1.6 m and the standard deviation, s is 0.05 m, the height of...

Variability: Analysis

Variability: Analysis

Measures of variability are statistical metrics that reveal the dispersion pattern within a dataset. They are pivotal in biostatistics, providing insights into the heterogeneity within health and biological data. Variability signifies the degree to which data points diverge from one another, helping researchers understand the potential range of values and associated uncertainty within the data.
The range is a simple measure of variability, indicating the difference between the highest and...

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Related Experiment Video

Updated: Jul 14, 2026

Making Record-efficiency SnS Solar Cells by Thermal Evaporation and Atomic Layer Deposition

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Save money by understanding variance and tolerancing.

¹Team Consulting Ltd, Ickleton. Cambridge, UK. stuart.kay@team-consulting.com

Medical Device Technology

|June 26, 2007

Summary

Understanding manufacturing variance and tolerancing is crucial. This study presents a methodology for correct tolerance allocation to reduce production costs and improve product quality.

Area of Science:

Manufacturing Engineering
Industrial Engineering
Quality Control

Background:

Manufacturing processes exhibit inherent variability, leading to component and assembly deviations.
Misapplication of design tolerances due to inadequate understanding of process capability and variance can escalate costs and quality issues.

Purpose of the Study:

To introduce a systematic methodology for accurate tolerance allocation in manufacturing.
To prevent increased tooling expenses, inflated production costs, and high reject rates.

Main Methods:

Describing a methodology for precise tolerance allocation.
Detailing appropriate analytical techniques for variance assessment.

Main Results:

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The proposed methodology enables correct tolerance allocation.

Implementation can mitigate risks associated with incorrect tolerances, such as product recalls and warranty claims.

Conclusions:

Accurate tolerance allocation is essential for cost-effective manufacturing.
Understanding and managing process capability and variance are key to optimizing product quality and reducing financial losses.