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Statistics Calculators ▶ Coefficient Of Variation Calculator

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**Table of Content**

This coefficient of variation calculator helps to calculate coefficient of variation corresponding to the given date set values. The coefficient of variance is the ratio of the standard deviation to the mean.

For instance, the standard deviation is 17% of the mean, is a coefficient variance. This tool allows you to calculate coefficient of variation of continuous data or binomial data.

The (CV) indicate as a statistical measure of the dispersion of data points in a data series around the mean. According to probability theory and statistics, it is the ratio of the standard deviation to the mean, and also known as relative standard deviation (RSD). In other words, CV is the measure of relative variability.

As mentioned-above, CV is the ratio of the standard deviation to the mean, so:

**CV = σ/ μ**

Where;

CV = Coefficient of Variation

σ = Standard Deviation

μ = Mean

Formula to calculate Standard Deviation:

σ = √((∑▒〖(x- μ)^2 〗)/(n-1))

Formula to calculate Mean:

μ = (∑▒x)/n

**Problem:**

Find the coefficient of variance for the samples 62.25, 60.36, 64.28, 61.24, and 66.24 of a population.

**Solution:**

**First, calculate Mean:**

Mean = (62.25 + 60.36 + 64.28 + 61.24 + 66.24)/5

= 314.37/5

=62.874

**Second, calculate Standard Deviation:**

SD = √( (1/(5 – 1)) * 〖(62.25- 62.874)〗^2 + 〖(60.36- 62.874)〗^2 + 〖(64.28- 62.874)〗^2 + 〖(61.24 – 62.874)〗^2 + 〖(66.24- 62.874)〗^2)

= √( (1/(4) * 〖(-0.624)〗^2 + 〖(-2.514)〗^2 + 〖(1.406)〗^2 + 〖(-1.634)〗^2 + 〖(3.366)〗^2)

= √ ( (1/(4) * (0.389376) + (6.320196) + (1.976836) + (2.669956) + (11.329956)

= √5.67158

SD = 2.38150

Finally, Calculate (CV):

CV = Standard Deviation/ Mean

Put the values into the coefficient of variation equation:

= 2.38150/62.874

CV = 0.037877

**References:**

From Wikipedia, the free encyclopedia – According to The Theory And Statistics, The Coefficient of Variation (CV)