# Worksheet: Spearman's Rank Correlation Coefficient

In this worksheet, we will learn about Spearman's rank correltion coefficient. Spearman’s correlation coefficient can be calculated whether the data are quantitative or descriptive.

**Q1: **

The data shows the relation between a company’s production and its employees’ salaries in five years.

Production | 1,000 | 2,000 | 2,500 | 4,000 | 2,300 |
---|---|---|---|---|---|

Salaries | 150 | 200 | 250 | 700 | 180 |

Find the Spearman’s correlation coefficient between production and salaries.

**Q2: **

What type of data is Spearman’s rank correlation coefficient appropriate for?

- AContinuous and discrete data
- BDiscrete data
- CContinuous data

**Q3: **

Find the Spearman’s correlation coefficient between sales and advertising from the given data.

Advertising | 1,000 | 800 | 1,000 | 1,500 |
---|---|---|---|---|

Sales | 5,000 | 4,500 | 4,500 | 6,500 |

**Q4: **

Which of the following is the formula of Spearman’s rank correlation coefficient?

- A
- B
- C
- D
- E

**Q5: **

The following table represents the relation between sale and profit for six models of televisions.

Television Sale | 500 | 600 | 550 | 100 | 480 | 400 |
---|---|---|---|---|---|---|

Television Profit | 300 | 400 | 400 | 90 | 250 | 200 |

Find Spearman’s correlation coefficient between television sale and profit. Round your answer to three decimal places.

**Q6: **

Find Spearman’s correlation coefficient between and . Round your answer to three decimal places.

4 | 7 | 8 | 5 | 8 | 12 | |

7 | 6 | 6 | 4 | 6 | 10 |

**Q7: **

In a study of the relation between students’ grades in mathematics and science, the following results were found for six students.

Mathematics | D | B | A | B | D | D |
---|---|---|---|---|---|---|

Science | C | C | B | A | C | F |

Find the Spearman’s correlation coefficient. Round your answer to three decimal places.

**Q8: **

The following table represents the relation between the results of employees’ appraisal this year and last year.

Last Year | Meets expectations | Needs improvement | Exceptional | Meets expectations | Exceeds expectations |
---|---|---|---|---|---|

This Year | Exceeds expectations | Meets expectations | Exceptional | Needs improvement | Exceeds expectations |

Find the Spearman’s correlation coefficient between last and current years results.

**Q9: **

In a study to discover the relationship between the age of a mother and the number of her children, the following data were found.

Mother’s Age | 19 | 22 | 24 | 28 | 29 | 32 | 34 | 35 |
---|---|---|---|---|---|---|---|---|

Number of Children | 2 | 1 | 1 | 2 | 3 | 4 | 3 | 5 |

Find Spearman’s correlation coefficient. Round your answer to three decimal places.

**Q10: **

The table shows the relation between two variables, and . Find Spearman’s correlation coefficient between them, rounded to the nearest thousandth.

50 | 90 | 75 | 150 | 63 | 35 | 75 | 90 | 50 | |

130 | 130 | 64 | 80 | 100 | 55 | 80 | 100 | 80 |

**Q11: **

Using the information given in the table, find the Spearman’s rank correlation between the variables and . Give your answer to four decimal places.

Good | Excellent | Good | Excellent | Excellent | Excellent | |

Poor | Good | Poor | Excellent | Very Good | Good |

**Q12: **

Using the information from the table, find the Spearman’s rank correlation coefficient and determine the type of correlation between the age of a mother and number of children. Give the numerical part of your answer to four decimal places.

Age of Mothers (Years) | 24 | 27 | 35 | 24 | 35 | 21 | 35 | 33 |
---|---|---|---|---|---|---|---|---|

No. of Children (n) | 1 | 4 | 3 | 5 | 3 | 1 | 2 | 4 |

- A0.1845, inverse correlation
- B0.1845, direct correlation
- C0.2113, direct correlation
- D , inverse correlation

**Q13: **

Using the information from the table, find the Spearman’s rank correlation coefficient and determine the type of correlation between the variables and . Give the numerical part of your answer to four decimal places.

14 | 9 | 10 | 13 | 6 | 9 | |

21 | 20 | 23 | 16 | 20 | 16 |

- A0.2714, inverse correlation
- B0.3, direct correlation
- C0.2714, direct correlation
- D0.3, inverse correlation