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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?

  • A16𝑑(𝑛1)
  • B16𝑑𝑛(𝑛1)
  • C6𝑑𝑛(𝑛1)
  • D16𝑑𝑛(𝑛1)
  • E1𝑑𝑛(𝑛1)

Q2:

True or False: When the ranks of each two corresponding elements in two groups of data 𝑋 and 𝑌 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.

Production1,0002,0002,5004,0002,300
Salaries150200250700180

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)154263
Price ($)79160125105214103

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 𝑟=0 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.

MathematicsDBABDD
ScienceCCBACF

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 𝑥 and 𝑦. Give your answer to four decimal places.

𝑥GoodExcellentGoodExcellentExcellentExcellent
𝑦PoorGoodPoorExcellentVery GoodGood

Q9:

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

EmployeeABCDE
Last YearMeets expectationsNeeds improvementExceptionalMeets expectationsExceeds expectations
This YearExceeds expectationsMeets expectationsExceptionalNeeds improvementExceeds expectations

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

Q10:

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

𝑥 4 7 8 5 8 12
𝑦 7 6 6 4 6 10

This lesson includes 20 additional questions and 99 additional question variations for subscribers.

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