Number of samples = 5

Mean x = 20.6

Mean y = 15.2

Covariance(X,Y) = 146.1

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GENERATE WORK

GENERATE WORK

**Input Data : **

Data set x = 5, 12, 18, 23, 45

Data set y = 2, 8, 18, 20, 28

Total number of elements = 5

**Objective :**

Find what is correlation coefficient for given input data?

**Formula :**

**Solution :**

X_{mean} = (5 + 12 + 18 + 23 + 45)/5

= 103/5

X_{mean} = 20.6

Y_{mean} = (2 + 8 + 18 + 20 + 28)/5

= 76/5

Y_{mean} = 15.2

Cov(x, y) = ((5 - 20.6) x (2 - 15.2)) + (( 12 - 20.6) x ( 8 - 15.2)) + (( 18 - 20.6) x ( 18 - 15.2)) + (( 23 - 20.6) x ( 20 - 15.2)) + (( 45 - 20.6) x ( 28 - 15.2))(5 - 1)

= ((-15.6) x (-13.2)) + ((-8.6) x (-7.2)) + ((-2.6) x (2.8)) + ((2.4) x (4.8)) + ((24.4) x (12.8))4

= (205.92) + (61.92) + (-7.28) + (11.52) + (312.32)4

= 584.44

Cov(x, y) = 146.1

**Covariance calculator** - step by step calculation to measure the statistical relationship (linear dependence) between the two sets of population data, provided along with formula & solved example problems. In probability & statistics theory for data analysis, the calculation of covariance is important in many experiments to find the statistical relationship between two sets of data. The solved example problem helps user to understand how to calculate covariance to find the linear dependence between the data sets. Along with the results, user can also get the complete step by step calculation for the given values of input data.

The below formulas are used to find the covariance and the solved example problem underneath illustrates how the values are being used in the formulae

By using the above mathematical formulas, the following example problem for covariance calculation have been solved.

**Example Problem**

For the data sets X = 65.21, 64.75, 65.26, 65.76, 65.96 and Y = 67.25, 66.39, 66.12, 65.70, 66.64, find the covariance to estimate the linear relationship between the two data sets X & Y.

**Solution**

Sum(X) = 65.21 + 64.75 + 65.26 + 65.76 + 65.96

= 326.93

**μ _{x}** = 326.93 / 5

=

Sum(Y) =67.25 + 66.39 + 66.12 + 65.70 + 66.64 = 332.09

=

= (65.21 - 65.38) * (67.25 - 66.42) + (64.75 - 65.38) * (66.39 - 66.42) + (65.26 - 65.38) * (66.12 - 66.42) + (65.76 - 65.38) * (65.7 - 66.42) + (65.96 - 65.38) * (66.64 - 66.42))/4

=

In probability & statistics for data analysis, the covariance plays vital role in various applications. When it comes to verify or perform such calculations online, this covariance calculator may help users to make the calculations simple as possible. Also, it provides the complete step by step calculation for the given values to find the linear dependency (statistical relationship) between the two data sets.