My Learning Cart
?
Categories
Account

The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviat

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

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

Options:

  1. 2
  2. 3
  3. 4
  4. 5

Correct Answer: 2

Exam Year: 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).

The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviat

Practice Questions

Q1
The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)
  1. 2
  2. 3
  3. 4
  4. 5

Questions & Step-by-Step Solutions

The scores of five students are: 20, 22, 24, 26, 28. What is the standard deviation? (2020)
  • 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.
  • Mean – The average of a set of numbers, calculated by summing the values and dividing by the count.
  • Variance – A measure of how much the values in a set differ from the mean, calculated as the average of the squared differences from the mean.
  • Standard Deviation – The square root of the variance, representing the average distance of each data point from the mean.
Soulshift Feedback ×

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

Not likely Very likely
Home Practice Performance eBooks