if the mean of a set of data is 23.00, and 12.60 has a z-score of -1.30, then what is the standard deviation?
12.60 - 23.00 = A
A / -1.30 = standard deviation
Z = (score-mean)/Standard deviation
Fill in the respective values and solve for the SD.
To find the standard deviation, 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
- σ is the standard deviation
Given that the mean is 23.00 and 12.60 has a z-score of -1.30, we can plug these values into the equation:
-1.30 = (12.60 - 23.00) / σ
Now, we can solve for σ by rearranging the equation:
-1.30 * σ = 12.60 - 23.00
-1.30 * σ = -10.40
Next, divide both sides of the equation by -1.30 to isolate σ:
σ = (-10.40) / -1.30
σ = 8.00
Therefore, the standard deviation is 8.00.
To find the standard deviation, you need to know two pieces of information: the mean and the z-score of a specific value. In this case, you are given the mean of the data set (23.00) and the z-score of a particular value (12.60 with a z-score of -1.30). However, the standard deviation is not directly calculable using only this information.
The formula to calculate the z-score is:
z = (x - μ) / σ
Where:
- z is the z-score
- x is the value in question
- μ is the mean of the data set
- σ is the standard deviation
Since you are given the mean (μ), the value (x), and the z-score (z), you can rearrange the formula to solve for the standard deviation (σ).
Rearranging the formula, we have:
σ = (x - μ) / z
Substituting the given values:
σ = (12.60 - 23.00) / -1.30
Evaluating the expression:
σ = -10.40 / -1.30
σ ≈ 8.00
So, the standard deviation of the data set is approximately 8.00.