Calculating the Standard Deviations and Coefficient of Variation for a Set of Numbers

To calculate the standard deviations and coefficient of variation for a set of numbers, follow the steps below:

Step 1: Find the Mean
- Add up all the numbers in the set to get the sum.
- Divide the sum by the total number of values in the set to get the mean.

For the set of numbers 5, 8, 9, 2, 6:
- Sum = 5 + 8 + 9 + 2 + 6 = 30
- Mean = 30 / 5 = 6

Step 2: Find the Variance
- For each number in the set, subtract the mean and square the result.
- Add up all the squared differences.
- Divide the sum by the total number of values in the set minus 1 to get the variance.

For the set of numbers 5, 8, 9, 2, 6:
- (5 - 6)^2 = 1
- (8 - 6)^2 = 4
- (9 - 6)^2 = 9
- (2 - 6)^2 = 16
- (6 - 6)^2 = 0
- Sum of squared differences = 1 + 4 + 9 + 16 + 0 = 30
- Variance = 30 / (5 - 1) = 7.5

Step 3: Find the Standard Deviation
- Take the square root of the variance to get the standard deviation.

For the set of numbers 5, 8, 9, 2, 6:
- Standard deviation = √7.5 ≈ 2.74

Step 4: Find the Coefficient of Variation
- Divide the standard deviation by the mean and multiply by 100 to get the coefficient of variation.

For the set of numbers 5, 8, 9, 2, 6:
- Coefficient of variation = (2.74 / 6) x 100 ≈ 45.67%

Therefore, the standard deviation of the set of numbers 5, 8, 9, 2, 6 is approximately 2.74 and the coefficient of variation is approximately 45.67%.

SD = √(5-6)²+(8-6)²+(9-6)²+(2-6)²+(6-6)²
= √1+4+9+16/5 = √30/5 = √6= 2.45
CV = SD/mean×100 = 2.45/6×100 = 40.83