Stats I - Chapter 2 – Descriptive Techniques I
Descriptive statistic involves
- Arranging
- Summarizing
- Presenting
A set of data in such a way that useful information is produced
Its methods make use of graphical techniques and numerical descriptive measures (such as averages) to
summarize and present the data.
A variable is some characteristic of a population or sample.
- E.g. student grades.
- Typically denoted with a capital letter: X, Y, Z…
The values of the variable are the range of possible values for a variable.
- E.g. student marks (0..100)
Data are the observed values of a variable.
- E.g. student marks: {67, 74, 71, 83, 93, 55, 48}
Interval data
- Real numbers, i.e. heights, weights, prices, etc.
- Also referred to as quantitative or numerical.
- Arithmetic operations can be performed on Interval Data, thus its meaningful to talk about 2 x
Height, or Price + $1, and so on.
Nominal data
- The values of nominal data are categories of the data collected:
- E.g. responses to questions about marital status, coded as:
Single = 1, Married = 2, Divorced = 3, Widowed = 4
- 30 M and 45 F or 30 B and 45 G = Coding of nominal data
- Nominal data are only counts
These data are categorical in nature; arithmetic operations don’t make any sense (e.g. does Widowed ÷
2 = Married?!) Nominal data are also called qualitative or categorical
Ordinal Data
- appear to be categorical in nature, but their values have an order; a ranking to them:
E.g. College course rating system:
poor = 1, fair = 2, good = 3, very good = 4, excellent = 5
While it is still not meaningful to do arithmetic on this data (e.g. does 2*fair = very good?!), we can say
things like:
Excellent > poor OR fair < very good
Excellent greater than poor OR fair less than very good
That is, order is maintained no matter what numeric values are assigned to each category.
As mentioned above,
- All calculations are permitted on interval data.
- Only calculations involving a ranking process are allowed for ordinal data.
- No calculations are allowed for nominal data, save counting the number of observations in each
category.
This lends itself to the following “hierarchy of data”…
Hierarchy of Data
Interval
- Values are real numbers.
- All calculations are valid.
- Data may be treated as ordinal or nominal.
Ordinal
- Values must represent the ranked order of the data.
- Calculations based on an ordering process are valid.
- Data may be treated as nominal but not as interval.
Nominal
- Values are the arbitrary numbers that represent categories.
- Only calculations based on the f

More
Less