If the mean of a set of data is 20.00 and 12.20 has a z-score of -1.30, then the standard deviation must be: What formula would you use to determine this?
Z = (score-mean)/SD
-1.3 = (12.2-20)/SD
Solve for the SD.
10.14
To determine the standard deviation, you would use the formula for z-score:
z = (x - μ) / σ
Where:
z = z-score
x = given value
μ = mean
σ = standard deviation
Given information:
Mean (μ) = 20.00
Z-score (z) = -1.30
Value (x) = 12.20
Let's rearrange the formula to solve for the standard deviation:
z = (x - μ) / σ
Rearranging for σ:
σ = (x - μ) / z
Substituting the given values:
σ = (12.20 - 20.00) / -1.30
Now, we can calculate the standard deviation using the formula:
σ = (12.20 - 20.00) / -1.30
σ = -7.80 / -1.30
σ ≈ 6.00
Therefore, the standard deviation is approximately 6.00.