Final answer:
The standard deviation of the dataset {10, 20, 30, 40, 50} is approximately 14.1.
Step-by-step explanation:
The formula to calculate the standard deviation of a dataset is:
1. Find the mean of the dataset. In this case, the mean is 30.
2. Subtract the mean from each data point and square the result.
3. Find the mean of the squared differences.
4. Take the square root of the mean of the squared differences.
By using this formula, we can calculate the standard deviation of the dataset {10, 20, 30, 40, 50} as follows:
1. Mean = (10 + 20 + 30 + 40 + 50) / 5 = 30
2. Subtract the mean from each data point and square the result:
(10 - 30)^2 = 400
(20 - 30)^2 = 100
(30 - 30)^2 = 0
(40 - 30)^2 = 100
(50 - 30)^2 = 400
3. Find the mean of the squared differences:
(400 + 100 + 0 + 100 + 400) / 5 = 200
4. Take the square root of the mean of the squared differences:
Square root of 200 ≈ 14.1
Therefore, the standard deviation of the dataset {10, 20, 30, 40, 50} is approximately 14.1.