A set of 50 data values has a mean of 15 and a variance of 36.
Find the standard score of a data value = 30
Use Z equation.
Variance = SD^2
V = 30^2 = 900??
Go the opposite direction. If variance = SD^2, then SD = βvariance.
so the SD = 30??
To find the standard score (also known as the z-score) of a data value, you need to use the formula:
π§ = (π₯ - π) / π
Where:
π§ is the z-score,
π₯ is the data value,
π is the mean, and
π is the standard deviation.
In this case, you are given the mean (π = 15) and the variance (π^2 = 36), but you need the standard deviation.
To find the standard deviation, you need to take the square root of the variance. So:
π = β(36) = 6
Now you have all the values needed to calculate the z-score:
π§ = (π₯ - π) / π
π§ = (30 - 15) / 6
π§ = 15 / 6
π§ = 2.5
Therefore, the standard score (z-score) of a data value of 30 in this set is 2.5.