# Correlation between {1, 2, 3, 4 & 5} & {2, 1, 4, 3 & 7} Solved example problem, work with steps & calculation summary for correlation (r) between {1, 2, 3, 4 & 5} & {2, 1, 4, 3 & 7} to estimate the linear relationship or to find if the data linearly, non-linearly, positively or negatively correlated in statistical experiments.
Calculation Summary
Data set x{1, 2, 3, 4 & 5}
Data set y{2, 1, 4, 3 & 7}
Correlation Coefficient (r)0.8242

## Work with Steps for Correlation r = 0.8242

Users may refer the below example workout with steps to find if any correlation between dataset x = {1, 2, 3, 4 & 5} & y = {2, 1, 4, 3 & 7} or to learn the input parameters & values are being used in the calculation.

Workout :

step 1 Address the formula, input parameters and values
data set x = {1, 2, 3, 4 and 5}
data set y = {2, 1, 4, 3 and 7}
Total number of elements (n) = 5

step 2 Find x̄ & ȳ
x̄ = 15/5
x̄ = 3
ȳ = 17/5
ȳ = 3

step 3 To find coefficient correlation follow below the table

 x y X = x - x̄ Y = y - ȳ X2 Y2 XY 1 2 -2 -1.4 4 1.96 2.8 2 1 -1 -2.4 1 5.76 2.4 3 4 0 0.6 0 0.36 0 4 3 1 -0.4 1 0.16 -0.4 5 7 2 3.6 4 12.96 7.2 ∑x = 15 ∑y = 17 ∑X = 0 ∑Y = 0 ∑X2 = 10 ∑Y2 = 21.2 ∑XY = 12

step 4 Substitute ∑x, ∑y, ∑xy, ∑x2 & ∑y2 value in the below correlation coefficient formula

r = ∑XY∑X2. ∑Y2

∑XY = 12, ∑X2 = 10, ∑Y2 = 21.2

r = 1210 x 21.2

step 5 Simplify above expression

= 12212

= 1214.5602

r = 0.8242

Thus 0.8242 is the correlation between x = {1, 2, 3, 4 and 5} & y = {2, 1, 4, 3 and 7} 