Pearson's Correlation Coefficient (Grade 12)
Free printable Grade 12 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 12 · 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, 53), (2, 61), (3, 66), (4, 69), (5, 72). 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, 84), (1, 78), (2, 71), (3, 62), (4, 58), (5, 58). 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 5 cases: (1, 32), (2, 24), (3, 26), (4, 21), (5, 18). 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 5 cases: (1, 13), (2, 18), (3, 24), (4, 27), (5, 29). 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 5 cases: (0, 80), (1, 81), (2, 79), (3, 76), (4, 74). 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, 28), (4, 52), (6, 68), (8, 72), (10, 89), (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 = 0.18 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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