Suppose you did a survey of male shoes size and the mean of that survey was size 10 with a standard deviation of 1.5. What is the z-score of a size of 7.5?
To calculate the z-score of a specific value, we use the formula:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value you want to convert to a z-score
- μ is the population mean
- σ is the standard deviation of the population
In your case, the mean shoe size of males is μ = 10, and the standard deviation is σ = 1.5. You want to find the z-score for a shoe size of 7.5, so x = 7.5.
Substituting these values into the formula, we have:
z = (7.5 - 10) / 1.5
Calculating this equation gives us:
z = -2.5 / 1.5
z = -1.67
Therefore, the z-score of a shoe size of 7.5 is -1.67.
Z = (score-mean)/SD
Insert the values and calculate.