Measures of Variability or Dispersion Range - high and lows. –Limitations: Based on only two extreme observations Interquartile range - measures variablility.

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Measures of Variability or Dispersion Range - high and lows. –Limitations: Based on only two extreme observations Interquartile range - measures variablility based on percentiles. Q3(75th percentile) -Q1 (25th percentile) Limitations: Leaves our many observations Mean Deviation – the average of the absolute deviations. ∑|x-µ| / n Limitations: Less sensitive to deviations in the distribution Variance - Based on distances from the mean (X - mean). Takes the square of each deviation from the average and then averages the squares. ∑(x-µ) 2 / n Standard Deviation - the square root of the variance

Variance Formula

Standard Deviation How do we calculate the standard deviation?

SPSS uses the n-1 formula to calculate the standard deviation. Why do you think that is?

Homework #3 For homework #3 use the n-1 formula to calculate the variance and standard deviation. This will allow you to use SPSS to check your hand calculations

Why Do We Want a Measure of Variation? Which is the Better Measure of Variation? Why do we Square the difference from the mean? Why do we take the square root of the Variance? How do we interpret the Standard Deviation?