Final answer:
After calculating, the mean is determined to be 20, the variance is 50, and the standard deviation is approximately 7.07. Option (b) is the correct choice.
Step-by-step explanation:
To find the mean, variance, and standard deviation of the given dataset (10, 15, 20, 25, 30), we first need to calculate the mean:
- Add up all the numbers: 10 + 15 + 20 + 25 + 30 = 100.
- Divide the sum by the count of numbers: 100 / 5 = 20, so the mean is 20.
- To find the variance, subtract the mean from each number, square the result, and find the average of those squared differences:
- (10 - 20)² = 100
- (15 - 20)² = 25
- (20 - 20)² = 0
- (25 - 20)² = 25
- (30 - 20)² = 100
Add these squared differences: 100 + 25 + 0 + 25 + 100 = 250.Divide by the number of values (5): 250 / 5 = 50. So the variance is 50.The standard deviation is the square root of the variance: √50 ≈ 7.07.The correct answer from the given options is b) Mean: 20, Variance: 50, Standard deviation: 7.07.