I need to know the standard deviation and how to get it for the following set of numbers. {10, 11, 10, 12, 11, 10, 11, 11, 12, 13, 11, 10, 14}
The standard deviation is the sqrt(sum(mean - i)^2 / (n-1)), where i takes on the value of each element in the set, and n is the number of elements in the set.
Start by finding the mean. Then for each element in the set, find the difference from the mean and square it. Find the sum of those differences, divide it by (n-1), and take the square root.
In case you didn't understand Marth's directions, you need to find the sum of those squared differences.
Since the mean of any distribution is a fulcrum, the sum of the differences of individual scores from the mean always = 0.
I hope this helps a little more.
To calculate the standard deviation of a set of numbers, you need to follow these steps:
Step 1: Find the mean
To calculate the mean (average) of the given set of numbers, add up all the numbers in the set and divide the sum by the total count of numbers.
Mean = (10 + 11 + 10 + 12 + 11 + 10 + 11 + 11 + 12 + 13 + 11 + 10 + 14) / 13
Mean = 145 / 13
Mean = 11.15 (rounded to two decimal places)
Step 2: Calculate the deviation
The deviation is the difference between each number in the set and the mean. Subtract the mean from each number.
Deviation = {10 - 11.15, 11 - 11.15, 10 - 11.15, 12 - 11.15, 11 - 11.15, 10 - 11.15, 11 - 11.15, 11 - 11.15, 12 - 11.15, 13 - 11.15, 11 - 11.15, 10 - 11.15, 14 - 11.15}
Step 3: Square each deviation
Square each deviation calculated in step 2.
Squared Deviation = {(-1.15)^2, (-0.15)^2, (-1.15)^2, (0.85)^2, (-0.15)^2, (-1.15)^2, (-0.15)^2, (-0.15)^2, (0.85)^2, (1.85)^2, (-0.15)^2, (-1.15)^2, (2.85)^2}
Step 4: Calculate the variance
The variance is the average of the squared deviations. Add up all the squared deviations and divide the sum by the total count of numbers.
Variance = (1.3225 + 0.0225 + 1.3225 + 0.7225 + 0.0225 + 1.3225 + 0.0225 + 0.0225 + 0.7225 + 3.4225 + 0.0225 + 1.3225 + 8.1225) / 13
Variance = 18.62 / 13
Variance = 1.43 (rounded to two decimal places)
Step 5: Calculate the standard deviation
The standard deviation is the square root of the variance.
Standard Deviation = √1.43
Standard Deviation ≈ 1.20 (rounded to two decimal places)
Therefore, the standard deviation of the given set of numbers {10, 11, 10, 12, 11, 10, 11, 11, 12, 13, 11, 10, 14} is approximately 1.20.