To find the standard deviation of the data set, you can use the formula:
σ = √[Σ(x - μ)² / N]
Where:
- σ is the standard deviation
- Σ is the sum of
- x is each value in the data set
- μ is the mean of the data set
- N is the number of values in the data set
First, find the mean of the data set:
μ = (2 + 4 + 4 + 5 + 7 + 8 + 8 + 9 + 12 + 15 + 17 + 28) / 12 = 9.5
Next, calculate the sum of the squared differences between each value and the mean:
Σ(x - μ)² = (2 - 9.5)² + (4 - 9.5)² + (4 - 9.5)² + (5 - 9.5)² + (7 - 9.5)² + (8 - 9.5)² + (8 - 9.5)² + (9 - 9.5)² + (12 - 9.5)² + (15 - 9.5)² + (17 - 9.5)² + (28 - 9.5)² = 1018
Then, divide the sum by the number of values in the data set:
1018 / 12 = 84.83
Finally, take the square root of the result to find the standard deviation:
σ = √84.83 = 9.2
Therefore, the standard deviation of the data set is 9.2 (rounded to one decimal place).