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 find the z-score of a shoe size of 7.5, we'll use the formula:
Z = (X - μ) / σ
where:
Z is the z-score,
X is the individual shoe size,
μ is the mean of the shoe sizes, and
σ is the standard deviation of the shoe sizes.
In this case:
X = 7.5 (individual shoe size)
μ = 10 (mean of the shoe sizes)
σ = 1.5 (standard deviation of the shoe sizes)
Now, let's substitute these values into the formula:
Z = (7.5 - 10) / 1.5
Calculating this:
Z = -2.5 / 1.5
Z ≈ -1.67
Therefore, the z-score for a shoe size of 7.5 is approximately -1.67.
Z = (score-mean)/SD
Insert the values and calculate.