Number of samples = 5

Mean x = 4

Mean y = 49

σ_{x} = 2.7386

σ_{y} = 40.0625

Correlation coefficient = 0.9684

<embed />

GENERATE WORK

GENERATE WORK

**Input Data : **

Data set x = 1, 2, 4, 5, 8

Data set y = 5, 20, 40, 80, 100

Total number of elements = 5

**Objective :**

Find what is correlation coefficient for given input data?

**Solution :**

X_{mean} = (1 + 2 + 4 + 5 + 8)/5

= 20/5

X_{mean} = 4

Y_{mean} = (5 + 20 + 40 + 80 + 100)/5

= 245/5

Y_{mean} = 49

σ_{x} = √(1/5 - 1) x ((1 - 4)^{2} + ( 2 - 4)^{2} + ( 4 - 4)^{2} + ( 5 - 4)^{2} + ( 8 - 4)^{2})

= √(1/4) x ((-3)^{2} + (-2)^{2} + (0)^{2} + (1)^{2} + (4)^{2})

= √(0.25) x ((9) + (4) + (0) + (1) + (16))

= √(0.25) x 30

= √7.5

σ_{x} = 2.7386

σ_{y} = √(1/5 - 1) x ((5 - 49)^{2} + ( 20 - 49)^{2} + ( 40 - 49)^{2} + ( 80 - 49)^{2} + ( 100 - 49)^{2})

= √(1/4) x ((-44)^{2} + (-29)^{2} + (-9)^{2} + (31)^{2} + (51)^{2})

= √(0.25) x ((1936) + (841) + (81) + (961) + (2601))

= √(0.25) x 6420

= √1605

σ_{y} = 40.0625

ρ(x, y) = (1 - 4)(5 - 49) + ( 2 - 4)( 20 - 49) + ( 4 - 4)( 40 - 49) + ( 5 - 4)( 80 - 49) + ( 8 - 4)( 100 - 49) (5 - 1) x 2.7386 x 40.0625ρ(x, y) = (-3 x -44) + (-2 x -29) + (0 x -9) + (1 x 31) + (4 x 51)(4) x 2.7386 x 40.0625

ρ(x, y) = (132) + (58) + (0) + (31) + (204)(438.8622)

ρ(x, y) = 425(438.8622)

ρ(x, y) = 0.9684

**correlation coefficient calculator** - to measure the degree of dependence or linear correlation (statistical relationship) between two random samples or two sets of population data. The measure of correlation generally represented by **(ρ)** or **r** is calculated with the sample mean and standard deviations of two sets of population data. In statistics, the well known method to find the dependence between the samples of two sets of population data is Pearson correlation coefficient. It measures the how strongly and in which direction the linear relationship between the the two data sets.

In statistical data analysis, the below formulas are used to find the correlation between the data sets. The *step by step calculation for correlation coefficient example* illustrates how the values are being used in the formula to find the linear correlation between the data sets.

Correlation Coefficient is a vital aspect used in statistics to calculate the strength and direction of the linear relationship or the statistical relationship (correlation) between the two population data sets. In the formula, the symbols **μ _{x}** and

1. Find the sample mean **μ _{x}** for data set X.

2. Find the sample mean

3.

4. Estimate the sample deviation

5.

6. Apply the values in the formula for correlation coefficient to get the result.

The CV value ranges between -1 to +1. The positive and negative correlation coefficient represents the direct (positive) and inverse (negative) linear correlation or statistical relationship between the data sets respectively. If it is close to zero or equal to zero then the data sets has no correlation (uncorrelated). If the value is lies between -1 to +1 then there is the linear correlation between the two data sets. The population data dependency is used in various applications, therefore when it comes to verify or perform such calculations online, this correlation coefficient calculator may help you to make your calculations as simple as possible.