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Midterm

MGMT 1050 Midterm: Mgmt 1050 Notes 4
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4 Pages
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Fall 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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Description
find more resources at oneclass.com 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 find more resources at oneclass.com find more resources at oneclass.com - the proportion of observations in any sample or population that lie within k standard deviations of the mean is at least - 1 – 1/k^2 for k>1 - When k = 2, chebysheff’s theorem states that at least three quarters (75%) of all observations lie within two standard deviations of the mean. With k = 3, chebysheff’s theorem states that at least eight-ninths (88.9%) of all observations lie within three standard deviations of the mean - Note that empirical rule provides approximate proportions, whereas Chebysheff’s theorem provides lower bounds on the proportions contained in the intervals Coefficient of Variation - Is a standard deviation of 10 a large number indicating great variability or a small number indicating little variability? The answer depends somewhat on the magnitude of the observations in the data set. If the observations are in the millions, then a standard deviation of 10 will probably be considered a small number - The coefficient of variation of a set of observations is the standard deviation of the observations divided by the mean - When data comes from very different populations it is useful to use COV – express the S.D relative to the mean Measure of Variability for Ordinal and Nominal Data - The measures of variability in this section can be used only for interval data - There are no measures of variability for nominal data Factors that identify when to compute the Range, Variance, Standard Deviation, and Coefficient of variation 1. Objective: describe a single set of data 2. Type of data: interval 3. Descriptive measurement: Variability Percentile - The Pth percentile is the value for which P percent are less than that value and (100- P)% are greater
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