Standard Deviation Variance and Range

Standard Deviation:  Typical distance of observations from their mean  A numerical summary that measures the spread of a distribution  A number that measures how far away the typical observation is from the center of distribution

Standard Deviation:  A low standard deviation means that the data is very closely related to the average  A high standard deviation means there is a large variance between data and the statistical average

Variance:  Way of measuring spread  Standard deviation is preferred over variance because the units in variance are always squared  Implies that units used to measure spread are different from units to measure center  Closely related to standard deviation

 Variance= (Standard Deviation)²  Standard deviation= √Variance  Example: If SD is 5, what is the variance? =25  If Variance is 16, what is SD? =4

Range:  Another measure of variability  Similar to IQR  Range is the distance spanned by the entire data set  Largest value minus the minimum value  Range= Maximum – Minimum

Range Cont.  Example:  Heights of 8 children in inches  48, 48, , 54, 60, 62, 71  Maximum – minimum. 71 – 48= 23 inches  Quick measurement of variability  Sensitive to peculiarities