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
-1.3σ = (12.20-20.00)
σ = 6.00
jskms
To calculate the standard deviation in this scenario, we can use the formula for z-score:
z = (x - μ) / σ
where z is the z-score, x is the value in question, μ is the mean, and σ is the standard deviation.
Given that the mean of the data set is 20.00, and 12.20 has a z-score of -1.30, we can substitute these values into the formula:
-1.30 = (12.20 - 20.00) / σ
Now, we can solve for σ by isolating it:
-1.30σ = 12.20 - 20.00
-1.30σ = -7.80
Dividing both sides of the equation by -1.30:
σ = -7.80 / -1.30
σ ≈ 6.00
Therefore, the standard deviation must be approximately 6.00.