Pearson's Correlation Coefficient (Grade 11)
Free printable Grade 11 General Mathematics worksheet: calculate and interpret Pearson's correlation coefficient r for bivariate data (ACMGM054). Every r computed from the data.
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Grade 11 · Math worksheet
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Date
Math
Bivariate Data: Pearson's Correlation Coefficient (Year 11-12 General Mathematics)
Calculate Pearson's correlation coefficient r for each data set and describe the strength and direction of the linear association. Strength bands: |r| at least 0.75 strong, 0.5 to 0.75 moderate, 0.25 to 0.5 weak, below 0.25 very weak. Answers are computed from the data.
- 1.The table records hours spent studying (x, hours) and exam mark (y, %) for 5 cases: (1, 50), (2, 59), (3, 68), (4, 74), (5, 70). Calculate Pearson's correlation coefficient r (to 3 decimal places) and describe the strength and direction of the linear association.
- 2.The table records hours of TV watched per day (x, hours) and test score (y, %) for 6 cases: (0, 79), (1, 82), (2, 73), (3, 65), (4, 56), (5, 49). Calculate Pearson's correlation coefficient r (to 3 decimal places) and describe the strength and direction of the linear association.
- 3.The table records age of the car (x, years) and resale value (y, $000) for 6 cases: (1, 27), (2, 27), (3, 21), (4, 21), (5, 16), (6, 17). Calculate Pearson's correlation coefficient r (to 3 decimal places) and describe the strength and direction of the linear association.
- 4.The table records fertiliser applied (x, kg) and crop yield (y, tonnes) for 6 cases: (1, 14), (2, 20), (3, 21), (4, 24), (5, 32), (6, 30). Calculate Pearson's correlation coefficient r (to 3 decimal places) and describe the strength and direction of the linear association.
- 5.The table records hours of exercise per week (x, hours) and resting heart rate (y, bpm) for 6 cases: (0, 86), (1, 81), (2, 72), (3, 77), (4, 73), (5, 63). Calculate Pearson's correlation coefficient r (to 3 decimal places) and describe the strength and direction of the linear association.
- 6.The table records number of deliveries (x, deliveries) and time spent on the road (y, min) for 6 cases: (2, 30), (4, 50), (6, 63), (8, 73), (10, 93), (12, 98). Calculate Pearson's correlation coefficient r (to 3 decimal places) and describe the strength and direction of the linear association.
- 7.A study reports a correlation coefficient of r = -0.42 between two numerical variables. Describe the strength and direction of the linear association.
- 8.A study reports a correlation coefficient of r = -0.91 between two numerical variables. Describe the strength and direction of the linear association.
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