~Descriptive stats describe a group of people (a "Sample")

~They help us to make sense of the information (scores or numbers) we have obtained from a "sample" of people

~Descriptive stats help us to:
     -summarize the "data" we have collected
     -make sense of the scores (data) we collected
     -organize our measurements/data into a comprehendible form
     -understand large amounts of data/scores/numbers

~In order to make some sense of this disorganized collection of scores from the sample (called "data set"), we often place them in pictorial form...a graph.
 

There are some general, helpful terms to describe the appearance of the graphed data (in comparison with the "normal" or "bell" curve):

1. Skew - The "lop-sidedness" of the distribution (shown on a graph)
2. Kurtosis - The amount of "peak" or "pointiness" of the graphed distribution of scores

~There are other terms/concepts/procedures that help us to describe this group of people:

1. Measures of Central Tendency (Ways to identify "the average score" in of a distribution)
 -Mean - the arithmetic mean (sum of scores divided by the number of scores in the distribution)
 -Median - the middle score when you line them up in order
 -Mode  - the most often obtained score in the distribution

2. Measures of Dispersion (How "spread out" the scores are...)
 -Range - How far between the highest and lowest score
 -Standard deviation - a marker point for determining difference from others.
 

What do you mean: "add 1"?
Why do it?
Why not just subtract lowest score from highest?
**Because all numbers in your distribution of scores must be represented and counted.
 

For example, consider this distribution and figure "the range" of scores
                 1, 2, 3, 4, 5

If you just subtracted the smallest number from the largest: "5 - 1" would be "4".  But count the number of scores with which you were provided...there are 5 of them (1,2,3,4,5).  A "range of 4" would not include both lowest (1) and highest (5) scores in the range.  That's why we add a "1".
 
 
 

Your turn:

What is the range (text book formula AND other formula) for this distribution of spelling test scores?

  100,  99,  98,  97,  94,  92, 91
 
 
 
 

Range = (100 - 91) +1
Range = 10
 
 

Calculate the "mean" for the following data set (add up all the scores and divide by the number of scores in your distribution set):
19
10
22
17
14
9
15
15
15
20
15
21

X = 16

Did anyone earn a score that was the mean?  No
 

Identify the "mode" of the distribution (identify the most common/often obtained score).
 

Identify the "median" of the distribution (the middle score in the distribution when they are lined up in order from smallest to largest).

Tom McIntyre at www.BehaviorAdvisor.com