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Midterm

MGMT 1050 Study Guide - Midterm Guide: Standard Deviation, Level Of Measurement, PercentilePremium

4 pages22 viewsFall 2014

Department
Management
Course Code
MGMT 1050
Professor
Olga Kraminer
Study Guide
Midterm

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One objective of statistical inferences is to estimate the parameter from the statistic
Deviation = (xi x(mean))
Deviation squared = (xi x(mean))^2
Variation = sum of deviation squared/n-1
Some deviations are mean and positive but when you add them all together it will be 0,
which is why we use deviation squared to avoid the “cancelling effect”
-is it possible avoid the cancelling effect without squaring? We could average the absolute
value of the deviations. This is called the mean absolute deviation
Interpreting the Variance
- The variance is useful when comparing two or more sets of the same type of variable
- If the variance of one data set is larger than that of a second data set, we interpret that
to mean that the observations in the first set display more variation than the
observations in the second set
- The problem of interpretation is caused by the way the variance is computed
- the problem of the interpretation is caused by the way the variance is computed
- we resolve this difficult by calculating another related measure of variability
- the standard deviation is simply the positive square root of the variance
- to gauge the consistency, we must determine the standard deviation (we could also
compute the variances)
Interpreting the Standard deviation
- if the histogram is bell shaped, we can use the empirical rule
Empirical Rule
1. approximately 68% of all the observations fall within one standard deviation of the
mean
2. approximately 95% of all the observations fall within two standard deviations of the
mean
3. approximately 99.7% of all the observations fall within three standard deviations of
the mean
A more general interpretation of the standard deviation is derived from chebysheff’s
theorem, which applies to all shapes of histograms
Chebysheff’s Theorem
- Chebysheff’s theorem applies to all shapes histograms
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