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These notes are not meant to be inclusive of all the information we will cover.   I created a PowerPoint presentation to teach some of the concepts covered in this unit.

There are three different MEASURES of CENTRAL TENDENCY (check out this link)
(Ways to be average)

MEASURES of VARIATION (Spread)

YOU CAN EASILY CALCULATE THE MEAN AND STANDARD DEVIATION WITH EXCEL.


Properties of the Normal Distribution


  1. Unimodal (one mode)
  2. Symmetrical (left and right halves are mirror images)-- just as many people above the mean as below the mean
  3. Bell shaped (maximum height (mode) at the mean)
  4. Mean, Mode, and Median are all located in the center
  5. Asymptotic (the further the curve goes from the mean, the closer it gets to the X axis; but the curve never touches the X axis)

AREA UNDER the NORMAL CURVE

Visit http://davidmlane.com/hyperstat/z_table.html to use an on-line program that will calculate areas under the normal curve. I also have a PowerPoint presentation on how to use his z table program.


Please check this link on STANDARDIZED SCORES to learn why they are meaningful

A z score indicates the number of standard deviations a corresponding raw score is above or below the mean
z score --> subtract the mean from the raw score and divide that answer by the standard deviation
(i.e., raw score=5, mean=8, standard deviation=2 --> 5 - 8 = -3 --> -3 divided by 2 = -1.5)

T score (transformed score -- a.k.a. Z score) --> multiple the z score by 10 and add 50
(i.e., z score=-1.5 --> -1.5 X 10 = -15 --> -15 + 50 = 35)


 

Scores don't always form a normal distribution


The skew is the tail. If the tail (skew) is on the left (negative side), we have a negatively skewed distribution. That means that more of the subjects scored on the high end (because most of the people are not in the tail where the low scores are)..

If the skew (tail) is on the right (positive side), we have a positive skew. That means more people scored low (because most of the people are not in the tail where the high scores are).


Sometimes most of the scores are in the middle, we then have a leptokurtic distribution. 

Sometimes the scores have a large spread without a lot of people in the middle, we then have a platykurtic distribution.

If a set of scores does not form a normal distribution (skewed), then the characteristics of the normal curve do not apply. For example, 68% of the scores would not fall within one standard deviation of the mean if the distribution were negatively skewed.


Del Siegle, Ph.D.
Neag School of Education - University of Connecticut
del.siegle@uconn.edu

www.delsiegle.com