Ch. 4: Measures of Variability
What do measures of variability convey? What information do they obtain?
-It is a single number used to describe how much variation and diversity there is in a distribution. -Information on how scores are spread from the center of a distribution
What measure of variation is best for each level of measurement?
-Ordinal: IQR with median alongside to be interpreted as the range of rank-ordered values in the middle 50% of the data -Interval-ratio level: Any but variance and SD are typically preferred.
What steps are taken to calculate standard deviation?
1) Calculate the mean (Y-bar=∑(Y)/N 2) Subtract mean from each score to find the deviation 3) Square each deviation 4) Sum the squared deviations 5) Divide the sum by N-1 6) Take the square root of the sum =Standard Deviation
What steps are taken to calculate variance?
1) Calculate the mean (Y-bar=∑(Y)/N 2) Subtract mean from each score to find the deviation 3) Square each deviation 4) Sum the squared deviations 5) Divide the sum by N-1 =variance
Standard deviation
A measure of variation for interval-ratio variables; it is equal to the square root of the variance/the square root of the average of the squared deviations from the mean.
Variance
A measure of variation for interval-ratio variables; it is the average of the squared deviations from the mean.
Measure of variability
Numbers that describe diversity or variability in the distribution of a variable.
What is the simplest and most straightforward measure of variability?
Range: Measures variation in interval-ratio level variables. Difference between highest/maximum scores and lowest/minimum scores in distribution.
Match the symbols in the variance equation to their meanings.
S²γ: the variance (Y-Y-bar): the deviation from the mean ∑(Y-Y-bar)²: sum of squared deviations from the mean N: number of scores
Interquartile range
The width of the middle 50% of the distribution. It is defined as the difference between the lower and upper quartiles (Q3-Q1). 75th percentile-25th percentile.
