If the mean of a set of data is 21.00, and 6.00 has a z score of –1.50, then the standard deviation must be
Use z-score equation:
z = (x - mean)/sd
z = -1.50
x = 6
mean = 21
Solve the equation for sd.
5.00
To determine the standard deviation, we need to use the z-score formula:
z = (X - μ) / σ
where
z is the z-score,
X is the value of the data point,
μ is the mean, and
σ is the standard deviation.
In this case, we know the mean (μ) is 21.00 and a specific data point has a z-score of -1.50. We can rearrange the formula to solve for the standard deviation (σ):
σ = (X - μ) / z
Substituting the given values:
σ = (6.00 - 21.00) / (-1.50)
Simplifying:
σ = -15.00 / -1.50
σ = 10.00
Therefore, the standard deviation must be 10.00.