PS296 Chapter Notes - Chapter 4: Unimodality
The Mean:
-sum of the scores divided by the number of scores
-designated by X bar = x̅
(x̅) = ΣX
N
-the mean and median will be close whenever the distribution is nearly symmetric
-when distribution is nearly symmetric and unimodal, the mode will also be in general
agreement
-the most common measure
Advantages:
-it can be manipulated algebraically because we can write an equation that defines the
mean
-cannot write a standard equation for the mode or median
-more stable estimate
Disadvantages:
-influenced by extreme scores
-value may not actually exist in the data
Document Summary
Sum of the scores divided by the number of scores. Designated by x bar = x (x ) = x. The mean and median will be close whenever the distribution is nearly symmetric. When distribution is nearly symmetric and unimodal, the mode will also be in general agreement. It can be manipulated algebraically because we can write an equation that defines the mean. Cannot write a standard equation for the mode or median. Value may not actually exist in the data. Interpretation in terms of underlying variable being measured requires some faith in the interval properties of the data. If we have a badly skewed distribution/heavy tailed distribution (one w unusual number number of large or small values), repeated samples from that population would have sample means that vary a great deal from one another. Trimmed means are calculated by taking one or more of the largest and smallest values, setting them aside, and taking the mean of what remains.
