# Correlation

## About correlation

Purpose – To measure the relationship between two variables. Students will normally learn the formula in calculating correlation in A-level mathematics class. However, the basic concept on the correlation which is the scatter plot maybe be introduce during the O-level mathematics lessons.

## Formula

Correlation = Covariance of the two variables, x & y and divide it by the standard deviation of x and standard deviation of y.

## How to determine the siginificance of the correlation value

Taking the sample size, n, then minus it with 2 in order to obtain the degree of freedom in order to obtain the critical value from the statistics table. df = n – 2.

**Question**

Calcuate the correlation values for the following set of the variables.

1. The correlation between Variable 1 & Variable 2.

variable 1 | variable 2 |

1 | 4 |

1 | 4 |

4 | 2 |

3 | 4 |

5 | 1 |

4 | 2 |

1 | 2 |

0 | 0 |

1 | 1 |

5 | 3 |

4 | 2 |

4 | 4 |

5 | 5 |

0 | 4 |

2. The correlation between Variable 3 & Variable 4.

variable 3 | variable 4 |

4 | 4 |

5 | 2 |

1 | 1 |

1 | 2 |

5 | 0 |

0 | 0 |

5 | 2 |

1 | 3 |

5 | 0 |

1 | 2 |

5 | 4 |

5 | 3 |

3 | 4 |

2 | 2 |

3. The correlation between Variable 5 & Variable 6.

variable 5 | variable 6 |

1 | 1 |

5 | 5 |

3 | 3 |

3 | 4 |

2 | 3 |

5 | 1 |

3 | 2 |

2 | 1 |

2 | 5 |

5 | 3 |

4 | 4 |

4 | 4 |

4 | 5 |

4 | 5 |

4. The correlation between Variable 7 & Variable 8.

variable 7 | variable 8 |

5 | 2 |

5 | 4 |

3 | 0 |

1 | 5 |

0 | 2 |

3 | 5 |

2 | 3 |

5 | 2 |

2 | 5 |

1 | 2 |

5 | 1 |

2 | 5 |

0 | 5 |

2 | 1 |

5. The correlation between variable 9 & variable 10.

variable 9 | variable 10 |

5 | 1 |

1 | 5 |

1 | 1 |

4 | 4 |

3 | 4 |

0 | 0 |

3 | 2 |

4 | 2 |

5 | 1 |

0 | 2 |

3 | 4 |

4 | 3 |

2 | 3 |

4 | 5 |

**Answer**

*Correlation between variable 1 & variable 2 = 0.129**Correlation between variable 3 & variable 4 = 0.16**Correlation between variable 5 & variable 6 = 0.335**Correlation between variable 7 & variable 8 = -0.304**Correlation between variable 9 & variable 10 = 0.138*

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