{-1, 0, 1, 2, -1, 0, 1, 2, -1, 0, 1, 2, 1, 1, -2} I need to find the standard deviation of this set of numbers please help!!!
See your other question on finding standard deviation.
To find the standard deviation of a set of numbers, you need to follow these steps:
Step 1: Find the mean (average) of the set.
To find the mean, add up all the numbers in the set and divide the sum by the total number of values. In this case, we have 15 values:
(-1 + 0 + 1 + 2 - 1 + 0 + 1 + 2 - 1 + 0 + 1 + 2 + 1 + 1 - 2) / 15 = 0
So, the mean is 0.
Step 2: Subtract the mean from each value and square the result.
Subtract the mean (0) from each value in the set and square the result. This step is done to remove any negative values and ensure that the variance is positive.
Squared differences: ( (-1-0)^2, (0-0)^2, (1-0)^2, (2-0)^2, (-1-0)^2, (0-0)^2, (1-0)^2, (2-0)^2, (-1-0)^2, (0-0)^2, (1-0)^2, (2-0)^2, (1-0)^2, (1-0)^2, (-2-0)^2 )
= (1, 0, 1, 4, 1, 0, 1, 4, 1, 0, 1, 4, 1, 1, 4)
Step 3: Find the mean of the squared differences.
Calculate the mean of the squared differences by summing all the squared differences that we obtained in step 2 and dividing by the total number of values.
Sum of squared differences: 1 + 0 + 1 + 4 + 1 + 0 + 1 + 4 + 1 + 0 + 1 + 4 + 1 + 1 + 4 = 24
Mean of squared differences: 24 / 15 = 1.6
Step 4: Take the square root of the mean of squared differences.
Finally, take the square root of the mean of squared differences to find the standard deviation:
Standard deviation = √(1.6) ≈ 1.2649
So, the standard deviation of the given set of numbers is approximately 1.2649.