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# Lesson Worksheet: Spearman’s Rank Correlation Coefficient Mathematics

In this worksheet, we will practice finding Spearman’s rank correlation coefficient.

**Q1: **

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

- A
- B
- C
- D
- E

**Q2: **

True or False: When the ranks of each two corresponding elements in two groups of data and are identical, Spearman’s rank correlation coefficient is equal to 1.

- ATrue
- BFalse

**Q3: **

The data shows the relation between a company’s production and its employees’ salaries in 5 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.

**Q4: **

Find the Spearman’s rank correlation coefficient between the product price and its lifetime from the given data. Round your answer to four decimal places.

Lifetime (yr) | 1 | 5 | 4 | 2 | 6 | 3 |
---|---|---|---|---|---|---|

Price ($) | 79 | 160 | 125 | 105 | 214 | 103 |

**Q5: **

The scatterplot shows the high jump and long jump results achieved by 15 competitors in the women’s heptathlon at the 2016 Olympics in Rio de Janeiro.

The correlation coefficient for this dataset is 0.859. What is the correct interpretation of this correlation coefficient?

- AThere is strong negative linear correlation between performance in the high jump and the long jump.
- BThere is no correlation or causation between high jump and long jump performance.
- CBeing good at the long jump causes a competitor to be better at the high jump.
- DThere is strong positive linear correlation between performance in the high jump and the long jump.
- EBeing good at the high jump causes a competitor to be better at the long jump.

**Q6: **

If the Spearman's correlation coefficient is calculated to be for two variables, then which of the following is true?

- AThere is no correlation between the two variables
- BThere is strong positive correlation between the two variables
- CThere is strong negative correlation between the two variables
- DThere is weak negative correlation between the two variables
- EThere is weak positive correlation between the two variables

**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: **

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 |

**Q9: **

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

Employee | A | B | C | D | E |
---|---|---|---|---|---|

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 the results of the last year and current year.

**Q10: **

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 |