PS296 Chapter Notes - Chapter 5: Standard Deviation, Squared Deviations From The Mean, Negative Number
Sample Variance (s²)
The score of the average deviation will be 0:
-some deviations will be negative
-others positive
-they will balance each other out
-when referring to population variance, we use σ²
-in the case of variance, we take advantage of the fact that the square of a negative
number is positive
-thus we sum the squared deviations rather than the deviations themselves
-we then divide that sum by a function of N – 1 for sample variance bc it leaves us with a
sample variance that is a better estimate of the corresponding population variance
-σ² is calculated by dividing the sum of the squared deviations by N rather than N-1 but
we rarely calculate a population variance
Calculating the mean absolute deviation
Definitional formulae:
s²x = Σ(x-x̄ ) ²
N-1
Document Summary
The score of the average deviation will be 0: When referring to population variance, we use . In the case of variance, we take advantage of the fact that the square of a negative number is positive. Thus we sum the squared deviations rather than the deviations themselves. We then divide that sum by a function of n 1 for sample variance bc it leaves us with a sample variance that is a better estimate of the corresponding population variance. Is calculated by dividing the sum of the squared deviations by n rather than n-1 but we rarely calculate a population variance. Bc its based on squared deviations, the result is in terms of squared units. Have little intuitive meaning with respect to the data. Solution is to take the square root of the variance. Standard deviation (s or ) is the positive square root of the variance.
