1. DESCRIPTIVE STATISTICS: GRAPHICAL AND NUMERICAL SUMMARIES
Scales of measurement
Measurements on members of the population – individuals
Qualitative or quantitative
Nominal scale Interval scale
Ordinal scale Ratio scale
Precision

2. Nominal and Ordinal scales
Nominal scale: individuals classified into groups depending on their attributes
EXAMPLE: Gender: M or F
Colors: White, Red, Blue.
Ordinal scale: Add order to nominal scale.
EXAMPLE: Grades: A, B, C, D, F
T-shirt size: S, M, L, XL.

3. Interval and Ratio scales
Interval scale:
mments are numerical values,
differences make sense,
intervals of equal length signify equal differences in the characteristic,
zero does not signify absence of the characteristic.
EXAMPLE: temperature.
Ratio scale:
like interval scale, but
has “absolute zero”, i.e. zero means absence of the characteristic.
EXAMPLE: height, weight.

4. GRAPHICAL SUMMARIES: qualitative variables
Bar chart
Example. According to the National Center for Health Statistics, the 6 leading causes of death in 1995 are: heart disease, cancer, stroke, pulmonary diseases, accidents, and others.
Cause of death
Count
(k)
percent
heart diseases
738
31.92
cancer
538
23.27
stroke
158
6.83
pulmonary diseases
103
4.46
accidents 93
4.02
others
682
29.5
All causes
2,312
100

5. GRAPHICAL SUMMARIES: qualitative variables
Pie chart. A disc (pie) is divided into “slices” proportional to the number of observations (frequency) in each category.
Relative frequency for each category. For example, heart disease 738/2312= of the total.
Angle corresponding to each category= relative frequency x 360. For heart disease, x 360=116 degrees.

6. GRAPHICAL SUMMARIES: Quantitative variables
HISTOGRAM: Shows frequency distribution – where the values are and how frequently they occur.
Example: Over 50 days a statistics course web site had the following number of “hits” per day: 20, 14, 21, …etc. (see text pg.14)
Frequency Table: relative frequency= frequency/total number of obs.
Class interval
Frequency
Relative frequency
0 -9 2
0.04
10-19 11
0.22
20 -29 17
0.34
30 -39 9
0.18
40 -49 6
0.12
50 -59 4
0.08
60-69 1
0.02
Total 50
1.00

7. GRAPHICAL SUMMARIES: Quantitative variables
Stem and leaf diagram. “ A bar chart drawn side ways”.
Stem: 1-2 leading digits.
Leaves: trailing (remaining) digits.
Example: Stem-and-leaf plot for the web site hits data
stem leaves
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