# 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 | X^{2} | Y^{2} | 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 | ∑X^{2} = 10 | ∑Y^{2} = 21.2 | ∑XY = 12 |

step 4 Substitute ∑x, ∑y, ∑xy, ∑x

^{2}& ∑y

^{2}value in the below correlation coefficient formula

r = ∑XY√∑X

^{2}. ∑Y

^{2}

∑XY = 12, ∑X

^{2}= 10, ∑Y

^{2}= 21.2

r = 12√10 x 21.2

step 5 Simplify above expression

= 12√212

= 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}