To find the standard deviation of the numbers 5, 4, 3, 2, and 1, we need to follow these simple steps:
Step 1: Calculate the mean (average) of the given numbers.
- Add the numbers together: 5 + 4 + 3 + 2 + 1 = 15.
- Divide the sum by the total number of values: 15 ÷ 5 = 3.
Therefore, the mean of the numbers is 3.
Step 2: Calculate the variance of the given numbers.
- Subtract the mean from each number: 5 - 3 = 2, 4 - 3 = 1, 3 - 3 = 0, 2 - 3 = -1, 1 - 3 = -2.
- Square each of the differences: 2^2 = 4, 1^2 = 1, 0^2 = 0, (-1)^2 = 1, (-2)^2 = 4.
- Add up the squared differences: 4 + 1 + 0 + 1 + 4 = 10.
- Divide the sum by the total number of values: 10 ÷ 5 = 2.
Therefore, the variance of the numbers is 2.
Step 3: Calculate the standard deviation of the given numbers.
- Take the square root of the variance: √2 = 1.41421356.
Therefore, the standard deviation of the numbers 5, 4, 3, 2, and 1 is approximately 1.41421356.