1. Descriptive statistics for groups:
How are statistics used … (a) to compare different groups and (b) to compare single individuals within any group?
Descriptive statistics for groups:
Measures of central tendency
Mean, Median and Mode
Measures of variability
Variance and Standard Deviation
Descriptive statistics for single scores:
Percentile rank and Z score

2. The same set of scores in rank order:
A set of scores, X (N=20):
The same set of scores in rank order:
Mode of X = 45
Median of X = 49.5

3. (Grouped) Frequency Distribution of X:5 4 3 2 1
Frequency
0-9
10-19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
Score (X) in intervals of 10
Interval
0 – 9
10 -19
20-29
30-39
40-49
50-59
60-69
70-79
80-89
90-99
Freq. 1 3 5 4 2

4. 1. Definition of the Mean (M):
2. Definitions of S2, called the variance or V, and S, called the standard deviation or SD:

5. X X - M (X - M)2
1. 58
2. 45
3. 23
4. 71 .
20. 57
( )
( )2 =
( )
( )2 =
( )
( )2 = 784
( )
( )2 = 400 .
( ) .
( )2 =
X = 1020
(X - M) = 0
(X - M)2 = 6400

6. Percentile rank (for a particular raw score):
...the percentage of all scores at or below that score.
Recipe:
1. Count the number of scores at or below its value.
2. Divide by the total number of the scores.
3. Multiply this result by 100.
For example in the illustrated data set, what is the percentile rank of the raw score, 23?
So “23” is at the 10th percentile.

7. Z score (for a particular raw score):
...the distance of that score from the mean, in units of “standard deviations.”
Recipe:
For any score, X,
For example in the illustrated data set, the raw score, 23, has the following Z score:
So “23” is 1.57 standard deviation units below the mean.