Solved Example
The below solved example with step by step calculation illustrates how the values are being used in the formulas to calculate the coefficient of variance.
Problem:
Calculate the relative variability (coefficient of variance) for the samples 60.25, 62.38, 65.32, 61.41, and 63.23 of a population
Solution:
Step by step calculation:
Step 1: calculate mean
Mean = (60.25 + 62.38 + 65.32 + 61.41 + 63.23)/5
= 312.59/5
= 62.51
Step 2: calculate standard deviation
= √( (1/(5 - 1)) * (60.25 - 62.51799)2 + (62.38 - 62.51799)2 + (65.32 - 62.51799)2 + (61.41 - 62.51799)2 + (63.23 - 62.51799)2)
= √( (1/4) * (-2.267992 + -0.137989992 + 2.802012 + -1.107992 + 0.712012))
= √( (1/4) * (5.14377 + 0.01904 + 7.85126 + 1.22764 + 0.50695))
= √ 3.68716
σ = 1.92
Step 3: calculate coefficient of variance
CV = (Standard Deviation (σ) / Mean (μ))
= 1.92 / 62.51
= 0.03071
The relative variability calculation is popularly used in engineering, physics, chemical industries etc. to employ the quality assurance. Therefore the coefficient of variance or relative standard deviation is widely used in various applications across the different types of industry. Any manual calculation can be done by using the above mathematical formulas. However, when it comes to online to measure the relative variability, this coefficient of variation calculator makes your calculation as simple as possible for the given sample data of the population.
Problem:
Calculate the relative variability (coefficient of variance) for the samples 60.25, 62.38, 65.32, 61.41, and 63.23 of a population
Solution:
Step by step calculation:
Step 1: calculate mean
Mean = (60.25 + 62.38 + 65.32 + 61.41 + 63.23)/5
= 312.59/5
= 62.51
Step 2: calculate standard deviation
= √( (1/(5 - 1)) * (60.25 - 62.51799)2 + (62.38 - 62.51799)2 + (65.32 - 62.51799)2 + (61.41 - 62.51799)2 + (63.23 - 62.51799)2)
= √( (1/4) * (-2.267992 + -0.137989992 + 2.802012 + -1.107992 + 0.712012))
= √( (1/4) * (5.14377 + 0.01904 + 7.85126 + 1.22764 + 0.50695))
= √ 3.68716
σ = 1.92
Step 3: calculate coefficient of variance
CV = (Standard Deviation (σ) / Mean (μ))
= 1.92 / 62.51
= 0.03071
The relative variability calculation is popularly used in engineering, physics, chemical industries etc. to employ the quality assurance. Therefore the coefficient of variance or relative standard deviation is widely used in various applications across the different types of industry. Any manual calculation can be done by using the above mathematical formulas. However, when it comes to online to measure the relative variability, this coefficient of variation calculator makes your calculation as simple as possible for the given sample data of the population.
Thanks for asking. The correct term is Slope OR the Regression Coefficient. For simple linear regression, which is represented by the equation of the regression line: ŷ = b0 + b1x, where b0 is a constant, b1 is the slope ( regression coefficient).
Can one statistic measure both the strength and direction of a linear relationship between two variables? Sure! Statisticians use the correlation coefficient to measure the strength and direction of the linear relationship between two numerical variables X and Y. The correlation coefficient for a sample of data is denoted by r.
Although the street definition of correlation applies to any two items that are related (such as gender and political affiliation), statisticians use this term only in the context of two numerical variables. The formal term for correlation is the correlation coefficient. Many different correlation measures have been created; the one used in this case is called the Pearson correlation coefficient.
The formula for the correlation (r) is
where n is the number of pairs of data;
are the sample means of all the x-values and all the y-values, respectively; and sx and sy are the sample standard deviations of all the x- and y-values, respectively.
You can use the following steps to calculate the correlation, r, from a data set:
- Find the mean of all the x-values
- Find the standard deviation of all the x-values (call it sx) and the standard deviation of all the y-values (call it sy).For example, to find sx, you would use the following equation:
- For each of the n pairs (x, y) in the data set, take
- Add up the n results from Step 3.
- Divide the sum by sx ∗ sy.
- Divide the result by n – 1, where n is the number of (x, y) pairs. (It’s the same as multiplying by 1 over n – 1.)This gives you the correlation, r.
For example, suppose you have the data set (3, 2), (3, 3), and (6, 4). You calculate the correlation coefficient r via the following steps. (Note that for this data the x-values are 3, 3, 6, and the y-values are 2, 3, 4.)
- Calculating the mean of the x and y values, you get
- The standard deviations are sx = 1.73 and sy = 1.00.
- The n = 3 differences found in Step 2 multiplied together are: (3 – 4)(2 – 3) = (– 1)( – 1) = +1; (3 – 4)(3 – 3) = (– 1)(0) = 0; (6 – 4)(4 – 3) = (2)(1) = +2.
- Adding the n = 3 Step 3 results, you get 1 + 0 + 2 = 3.
- Dividing by sx ∗ sy gives you 3 / (1.73 ∗ 1.00) = 3 / 1.73 = 1.73. (It’s just a coincidence that the result from Step 5 is also 1.73.)
- Now divide the Step 5 result by 3 – 1 (which is 2), and you get the correlation r = 0.87.