The mean is 18.1
The z-score for 13.0 is - 1.7.
What is the standard deviation for this data set.
Z = (score-mean)/SD
-1.7 = (13-18.1)/SD
-1.7 = -5.1/SD
-1.7SD = -5.1
SD = -5.1/-1.7
SD = 3.0
z-score = (given value - mean)/sd
-1.7 = (13 - 18.1)/sd
-1.7sd = -5.1
sd = -5.1/-1.7 = 3
Why did the statistician bring a ladder to the data set? Because it wanted to find a higher standard deviation!
But in all seriousness, to find the standard deviation, we can use the z-score formula:
z = (x - μ) / σ
Given that the mean (μ) is 18.1 and the z-score is -1.7, we can rearrange the formula to solve for the standard deviation (σ):
σ = (x - μ) / z
Plugging in the values, we get:
σ = (13.0 - 18.1) / (-1.7)
After calculating, we find that the standard deviation for this data set is approximately 2.94.
To find the standard deviation, you can use the formula:
z-score = (x - mean) / standard deviation
Given that the mean is 18.1 and the z-score for 13.0 is -1.7, we can rewrite the formula as:
-1.7 = (13.0 - 18.1) / standard deviation
Now, let's solve for the standard deviation:
-1.7 = -5.1 / standard deviation
To isolate the standard deviation, we can multiply both sides of the equation by -1:
1.7 = 5.1 / standard deviation
Next, we can divide both sides of the equation by 1.7 to solve for the standard deviation:
standard deviation = 5.1 / 1.7
Calculating this, we find:
standard deviation = 3
Therefore, the standard deviation for this data set is 3.
To find the standard deviation for this data set, we can use the formula that relates the z-score to the standard deviation:
z = (x - μ) / σ
where:
- z is the z-score
- x is the data value
- μ is the mean
- σ is the standard deviation
In this case, we are given the mean (μ = 18.1) and the z-score (-1.7) associated with a specific data value (13.0). We can rearrange the formula to solve for the standard deviation (σ):
σ = (x - μ) / z
Plugging in the values we have:
σ = (13.0 - 18.1) / -1.7
σ = -5.1 / -1.7
σ = 3
Therefore, the standard deviation for this data set is 3.