This question says: Statistical information for a data set is given.
-the mean is 18.1
-the z-score for 13.0 is -1.7
What is the standard deviation of this set?
Z = (score-mean)/SD
-1.7 = (13-18.1)/SD
-1.7SD = 13 - 18.1
Solve for SD.
To find the standard deviation of a data set, we need to use the z-score formula which relates the z-score, the mean, and the standard deviation. The formula is as follows:
z = (x - μ) / σ
Here,
z = -1.7 (given z-score for 13.0)
μ = 18.1 (mean)
x = 13.0 (given value)
Rearranging the formula to solve for the standard deviation (σ), we have:
σ = (x - μ) / z
Plugging in the given values, we get:
σ = (13.0 - 18.1) / -1.7
Calculating the above expression:
σ = -5.1 / -1.7
σ = 3
So, the standard deviation of this data set is 3.