11/07/2023
Calculate standard deviation: 2.345

Calculate the standard deviation of the set numbers, 2,5,6,7,3,8,9,8
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To calculate the standard deviation of a set of numbers, you need to follow these steps:
Find the mean (average) of the set.
Subtract the mean from each number and square the result.
Calculate the mean of the squared differences.
Take the square root of the mean calculated in step 3.
Let's calculate the standard deviation for the given set of numbers: 2, 5, 6, 7, 3, 8, 9, 8.
Step 1: Find the mean. Mean = (2 + 5 + 6 + 7 + 3 + 8 + 9 + 8) / 8 = 48 / 8 = 6
Step 2: Subtract the mean from each number and square the result. (2 - 6)^2 = 16 (5 - 6)^2 = 1 (6 - 6)^2 = 0 (7 - 6)^2 = 1 (3 - 6)^2 = 9 (8 - 6)^2 = 4 (9 - 6)^2 = 9 (8 - 6)^2 = 4
Step 3: Calculate the mean of the squared differences. Mean of squared differences = (16 + 1 + 0 + 1 + 9 + 4 + 9 + 4) / 8 = 44 / 8 = 5.5
Step 4: Take the square root of the mean calculated in step 3. Standard deviation = √5.5 ≈ 2.345
Therefore, the standard deviation of the set {2, 5, 6, 7, 3, 8, 9, 8} is approximately 2.345.
