The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)

Practice Questions

1 question

Questions & Step-by-step Solutions

1 item

Q: The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)

Solution: Mean = (20 + 22 + 24 + 26 + 28) / 5 = 24. Variance = [(20-24)² + (22-24)² + (24-24)² + (26-24)² + (28-24)²] / 5 = 8. SD = √8 = 2.83 (approximately 3).

Steps: 8

Step 1: Add all the scores together: 20 + 22 + 24 + 26 + 28.
Step 2: Calculate the total: 20 + 22 = 42, 42 + 24 = 66, 66 + 26 = 92, 92 + 28 = 120.
Step 3: Divide the total by the number of students (5) to find the mean: 120 / 5 = 24.
Step 4: Subtract the mean from each score to find the difference: 20 - 24 = -4, 22 - 24 = -2, 24 - 24 = 0, 26 - 24 = 2, 28 - 24 = 4.
Step 5: Square each difference: (-4)² = 16, (-2)² = 4, (0)² = 0, (2)² = 4, (4)² = 16.
Step 6: Add the squared differences together: 16 + 4 + 0 + 4 + 16 = 40.
Step 7: Divide the total of squared differences (40) by the number of students (5) to find the variance: 40 / 5 = 8.
Step 8: Take the square root of the variance to find the standard deviation: √8 ≈ 2.83.

The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)

Practice Questions

Questions & Step-by-step Solutions

Related Questions

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?