Difference between Variance and Standard Deviation

Difference between Variance and Standard Deviation

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Vikram
Vikram Singh
Assistant Manager - Content
Updated on Mar 14, 2023 04:34 IST

Variance and Standard Deviation are statistical measure to measure the dispersion of data point from the center or mean. In this article, we will discuss difference between variance and standard deviation.

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Variance and Standard Deviations are important statistical measurements that describe how items are distributed from each other and the center of the distribution. Such statistical measures are known as Measures of Dispersion. There are four methods to measure the dispersion in the data: Range, Interquartile Range, Variance, and Standard Deviations. This article will discuss the difference between Variance and Standard Deviation.

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Table of Content

Variance vs. Standard Deviation

Parameter Variance Standard Deviation
Definition Variance is the square deviation from the mean. Standard Deviation is the square root of the variance.
Measure Measures the dispersion of a dataset. Measures the spread of the data around the mean. 
Expressed in Squared Units Same units as the value in the dataset 

Read Also: Basic of Statistics for Data Science

Read Also: Measures of Dispersion

What is a Variance?

Definition

Variance is the average of the squared differences from the mean. It indicates how far individuals in a group are spread out.

  • When the Variance of the dataset is slight
    • It represents data points that are close to the mean.
  • When the Variance of the dataset is significant:
    • It represents data points are far away from the mean.

Formula of Variance

Population

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Sample

2023_03_formula-of-sample-variation.jpg

To know more about Population and Sample, read Introduction to Inferential Statistics

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What is Standard Deviation?

Definition

Standard Deviation measures how far a group of numbers is from the mean. It is useful to compare the spread of two separate datasets with approximately the same mean.

  • Standard Deviation is the square root of Variance.
  • Standard Deviation is very sensitive to extreme values.
  • If two datasets have the same mean but different standard deviations, then one with the higher SD will be more spread out from the center.
  •  If all the values in the dataset are equal, then the SD is zero.
  • A lower standard Deviation indicates data points in the dataset are dense near the mean.

Also Read: All about Symmetric Matrix

Formula of Standard Deviation

Population

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Sample

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Example

Example: Let there be two cricket players: Pant and Kartik, and you have to select one for the cricket world cup. The score of both the players in the last five T-20 matches are as follows:

Kartik Pant
23 34
28 85
45 02
59 15
63 77

Answer: Now, we will find the SD, and one who has the lesser value of SD will be more consistent.

Case -1: Kartik

Runs (xi) Squared Deviation  (xi– mean)2
23 (23 – 43.6)2
28 (28 – 43.6) 2
45 (45 – 43.6) 2
59 (59 – 43.6) 2
63 (63 – 43.6) 2
Mean = (23 + 38 + 45 + 59 + 63) / 5 = 43.6 Sum of Squared Deviation = 1283.2

Hence, Variance = s 2 = (sum of standard deviations) / n – 1 = 1283.2 / 5-1 = 1283.2/4 = 320.8

Hence, Standard Deviation = s = sqrt(variance) = sqrt (320.8) = 17.91

Now, similarly we will find the standard deviation of runs for Pant

Case 2: Pant

Runs (xi) Squared Deviation (xi– mean)2
34 (34 – 42.6) 2
85 (85 – 42.6) 2
02 (2 – 42.6) 2
15 (15 – 42.6) 2
77 (77 – 42.6) 2
Mean = 42.6 Sum of Squared Deviation = 5465.2

Hence, s2 = (sum of standard deviations) / n – 1 = 5465.2 / 5-1 = 5465.2/4 = 1366.3

Hence, s = sqrt(variance) = sqrt (1366.3) = 36.96

From above, the standard deviation of Kartik score is less than the pant, so Kartik is more consistent than Pant in scoring runs.

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Application

  • Machine Learning: Used in Hypothesis Testing and Confidence Interval
  • Finance: Used to understand how risky and volatile the investment is, stability of mutual funds
  • Forecasting: To make the weather forecast, projections about the company’s revenue
  •  Sports: Used to select the players in the team (As discussed in the above example.)

Key differences and similarities

  • Variance measures the dispersion of the dataset, while Standard Deviation measures the spread of the data around the mean.
  • Variance is the average squared difference from the mean, while standard Deviation is the square root of the Variance.
  • Standard Deviation is expressed in the same unit as the values in the dataset, while the Variance is expressed in a square unit. 
  • Both Standard Deviation and Variance are always positive.
  • If all the values in the dataset are equal, then both Variance and standard Deviation are zero.

Conclusion

In this article, we have discussed variance and standard deviations, their differences and example.

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FAQs

What is a Variance?

Variance is theu00a0average of the squared differences from the mean.u00a0It indicates how far individuals in a group are spread out.

What is a Standard Deviation?

Standard Deviation measures how far a group of numbers is from the mean. It is useful to compare the spread of two separate datasets with approximately the same mean.

How variance and standard deviation are related?

Standard Deviation is the square root of variance. Standard deviation helps to compare the value in the same unit as other measurement while variance give the squared unit.

When should you use variance instead of standard deviation?

Variance is mainly used to calculate the correlation and standard deviation is mainly used to analyze and compare the results.

What does a high variance and standard deviation mean?

High variance and high standard deviation indicate that dataset is more spread out from the mean that

About the Author
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Vikram Singh
Assistant Manager - Content

Vikram has a Postgraduate degree in Applied Mathematics, with a keen interest in Data Science and Machine Learning. He has experience of 2+ years in content creation in Mathematics, Statistics, Data Science, and Mac... Read Full Bio