Download Descriptive Statistics

Descriptive Statistics
I. Frequency Distributions
II. Measures of Central Tendency
III. Measures of Dispersion
I. Frequency Distributions
Frequency
– the number of observed cases for each value of the variable under observation
– EX:
N= 1,500
FEMALE:
MALE:
900
600
60%
40%
II. Measures of Central Tendency
A. MODE
– the value of a variable that is most frequently observed
B. MEDIAN
– the value of a variable that has 50% of the cases above it & 50% below it
C. MEAN
– the sum of the values for all cases divided by the number of cases --> “the average”
II. An Example
30
20
10
22
7
12
1
18
2
6
3
2
0
0
4
5
1
2
3
4
5
6
7
6
7
III. Measures of Dispersion
A. RANGE
– the difference between the highest observed value of a variable and the lowest
– in previous example
HIGH VALUE = 6
LOW VALUE = 1
RANGE = 5
– NOTE: Range doesn’t capture clusters of cases in middle or at extremes...
B. VARIATION
– sum of the squared deviations from the mean
C. VARIANCE
– variation divided by the number of cases
**for a sample population the denominator is N -1
D. STANDARD DEVIATION
– square root of the variance
III. (cont.) -> an example
x
x – x (x - x)2
4
-4
16
6
-2
4
8
0
0
9
1
1
10
2
4
11
3
9
TOTAL: 48
0
34
E. THE NORMAL DISTRIBUTION
– often called the “bell curve”
– the mean, median, & mode are identical
– a perfectly symmetrical distribution with most cases clustered around the mean
– 68% of the cases are within 1 standard deviation of the mean
– 95% are within 2 std. deviations
– 99.7% are within 3 std. deviations
A Normal Distribution
III. (cont.)
F. Z-SCORES
– a “raw score” expressed in standard deviations
– score’s deviation from the mean divided by the standard deviation
– useful for comparing scores (or measures) to rest of population of a nearly normal
distribution
– EX: Test Mean = 79.25; s = 7.19
SCORE = 95 --> 15.75 from mean
Z-SCORE = 2.19