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 1 6 𝑑 𝑛 ( 𝑛 1 )
  • B 6 𝑑 𝑛 ( 𝑛 1 )
  • C 1 6 𝑑 𝑛 ( 𝑛 1 )
  • D 1 𝑑 𝑛 ( 𝑛 1 )
  • E 1 6 𝑑 ( 𝑛 1 )

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 𝑥 and 𝑦 . Round your answer to three decimal places.

𝑥 4 7 8 5 8 12
𝑦 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, 𝐿 and 𝑀 . Find Spearman’s correlation coefficient between them, rounded to the nearest thousandth.

𝐿 50 90 75 150 63 35 75 90 50
𝑀 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 𝑥 and 𝑦 . Give your answer to four decimal places.

𝑥 Good Excellent Good Excellent Excellent Excellent
𝑦 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 0 . 2 1 1 3 , 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 𝑋 and 𝑌 . Give the numerical part of your answer to four decimal places.

𝑋 14 9 10 13 6 9
𝑌 21 20 23 16 20 16
  • A0.2714, inverse correlation
  • B0.3, direct correlation
  • C0.2714, direct correlation
  • D0.3, inverse correlation

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