Questions: The following is a list of measurements:
-4.42, 89, -88, -38, 52, 47, -59, -100, 57, 27
Suppose that these 11 measurements are respectively labeled 1, 2, ..., 11. (Thus -4 is labeled 1, 42 is labeled 2, and so on.) Complete the following:
M = (x - 12)^2
Transcript text: The following is a list of measurements:
-4.42, 89, -88, -38, 52, 47, -59, -100, 57, 27
Suppose that these 11 measurements are respectively labeled $1, 2, ..., 11$. (Thus -4 is labeled 1, 42 is labeled 2, and so on.) Complete the following:
M = (x - 12)^2
Solution
Solution Steps
Step 1: Calculate the Mean
The mean μ of the measurements is calculated using the formula:
μ=N∑i=1Nxi=1125≈2.27
Thus, the mean of the measurements is μ=2.27.
Step 2: Calculate the Variance
The variance σ2 is calculated using the formula:
σ2=n∑(xi−μ)2=3745.83
Therefore, the variance of the measurements is σ2=3745.83.
Step 3: Calculate the Standard Deviation
The standard deviation σ is the square root of the variance:
σ=3745.83≈61.2
Thus, the standard deviation of the measurements is σ≈61.2.
Step 4: Calculate M Values
The values of M for each measurement are calculated using the expression: