• Business
  • Finance
  • Banking
  • Education
  • General
  • Law
  • Science
  • IT
  • English

Key Differences

Know the Differences & Comparisons

Difference Between Variance and Standard Deviation

Last updated on February 13, 2020 by Surbhi S

variance vs standard deviationDispersion indicates the extent to which observations deviate from an appropriate measure of central tendency. Measures of dispersion fall into two categories i.e. an absolute measure of dispersion and relative measure of dispersion. Variance and standard deviation are two types of an absolute measure of variability; that describes how the observations are spread out around the mean. Variance is nothing but the average of the squares of the deviations,

Unlike, standard deviation is the square root of the numerical value obtained while calculating variance. Many people contrast these two mathematical concepts. So, this article makes an attempt to shed light on the important difference between variance and standard deviation.

Content: Variance Vs Standard Deviation

  1. Comparison Chart
  2. Definition
  3. Key Differences
  4. Illustration
  5. Similarities
  6. Conclusion

Comparison Chart

Basis for ComparisonVarianceStandard Deviation
MeaningVariance is a numerical value that describes the variability of observations from its arithmetic mean.Standard deviation is a measure of dispersion of observations within a data set.
What is it?It is the average of squared deviations.It is the root mean square deviation.
Labelled asSigma-squared (σ^2)Sigma (σ)
Expressed inSquared unitsSame units as the values in the set of data.
IndicatesHow far individuals in a group are spread out.How much observations of a data set differs from its mean.

Definition of Variance

In statistics, variance is defined as the measure of variability that represents how far members of a group are spread out. It finds out the average degree to which each observation varies from the mean. When the variance of a data set is small, it shows the closeness of the data points to the mean whereas a greater value of variance represents that the observations are very dispersed around the arithmetic mean and from each other.
For unclassified data: variance fformula for unclassified data

For grouped frequency distribution: variance formula for grouped frequency

Definition of Standard Deviation

Standard deviation is a measure that quantifies the amount of dispersion of the observations in a dataset. The low standard deviation is an indicator of the closeness of the scores to the arithmetic mean and a high standard deviation represents; the scores are dispersed over a higher range of values.
For unclassified data: std-dev-unclassifiedFor grouped frequency distribution: std-dev-grouped

Key Differences Between Variance and Standard Deviation

The difference between standard deviation and variance can be drawn clearly on the following grounds:

  1. Variance is a numerical value that describes the variability of observations from its arithmetic mean. Standard deviation is a measure of the dispersion of observations within a data set relative to their mean.
  2. Variance is nothing but an average of squared deviations. On the other hand, the standard deviation is the root mean square deviation.
  3. Variance is denoted by sigma-squared (σ2) whereas standard deviation is labelled as sigma (σ).
  4. Variance is expressed in square units which are usually larger than the values in the given dataset. As opposed to standard deviation which is expressed in the same units as the values in the set of data.
  5. Variance measures how far individuals in a group are spread out in the set of data from the average. Conversely, Standard Deviation measures how much observations of a data set differs from its mean.

Illustration

Marks scored by a student in five subjects are 60, 75, 46, 58 and 80 respectively. You have to find out the standard deviation and variance.
First of all, you have to find out the mean,

mean

So the average (mean) marks are 63.8
Now calculate the variance

XA(x-A)(X-A)^2
6063.8-3.814.44
7563.811.2125.44
4663.8-17.8316.84
5863.85.833.64
8063.816.2262.44

Where, X = Observations
A = Arithmetic Mean

varianceSo the variance is 150.56

And Standard deviation is – standard deviation

Similarities

  • Both variance and standard deviation are always positive.
  • If all the observations in a data set are identical, then the standard deviation and variance will be zero.

Conclusion

These two are basic statistical terms, which are playing a vital role in different sectors. Standard deviation is preferred over mean as it is expressed in the same units as those of the measurements while the variance is expressed in the units larger than the given data set.

Related Differences

  • Difference Between Recruiting and Staffing
  • Difference Between Cost Control and Cost Reduction
  • Difference Between Poll and Survey
  • Difference Between Capitalism and Communism
  • Difference Between Unqualified and Qualified Report

You Might Also Like:

standard deviation vs standard errorDifference Between Standard Deviation and Standard Error mean vs medianDifference Between Mean and Median t-test-vs-z-testDifference Between T-test and Z-test sample mean vs population meanDifference Between Sample Mean and Population Mean parameter vs statisticDifference Between Statistic and Parameter t-test vs f-testDifference Between T-test and F-test

Comments

  1. Ken says

    September 8, 2019 at 9:05 am

    Thank you for your effort

    Reply
  2. Anitha says

    October 23, 2019 at 4:20 pm

    Well explained, thank you

    Reply
  3. komal says

    November 3, 2019 at 9:58 am

    thank you very much

    Reply
  4. NCW says

    November 5, 2019 at 4:55 am

    Can you explain variance and standard deviation by using values of above example?

    Reply
  5. Mohammed Hamid Azmi says

    March 24, 2022 at 2:46 pm

    Very clear, good effort dear

    Reply
  6. RAJAN SEHGAL says

    June 13, 2022 at 4:53 am

    Explaining everything logical and simple way
    clear all doubts and make concepts crystal clear

    Reply

Leave a Reply Cancel reply

Your email address will not be published. Required fields are marked *

Top 5 Differences

  • Difference Between PERT and CPM
  • Difference Between Micro and Macro Economics
  • Difference Between Developed Countries and Developing Countries
  • Difference Between Management and Administration
  • Difference Between Qualitative and Quantitative Research

Related Differences

  • Difference Between Recruiting and Staffing
  • Difference Between Cost Control and Cost Reduction
  • Difference Between Poll and Survey
  • Difference Between Capitalism and Communism
  • Difference Between Unqualified and Qualified Report



New Additions

  • Difference Between Speak and Talk
  • Difference Between Economy Class and Business Class
  • Difference Between If and Whether
  • Difference Between Hotel and Motel
  • Difference Between FIR and Chargesheet
  • Difference Between Norms and Values
  • Difference Between Society and Community
  • Difference Between Sourcing and Procurement
  • Difference Between National Income and Per Capita Income
  • Difference Between Departmental Store and Multiple Shops
fb-follow youtube follow

Copyright © 2023 · Key Differences · Contact Us · About Us · Privacy