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School

York University
Department

Management

Course Code

MGMT 1050

Professor

Olga Kraminer

Study Guide

Midterm

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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