6.4 The Output
What does an empirical distribution represent?
How do we interpret the empirical distribution of PRICE variable?
6.4.1 Distribution I
To construct a histogram for continuous data,:
- divide the range of the data into intervals, which are usually called class intervals, cells, or bins.
- use the horizontal axis to represent the measurement scale for the data and the vertical scale to represent the counts, or frequencies.
- if the frequencies of each bin are divided by the total number of observations (\(n\)), then the vertical scale represents relative frequencies.
The blox plot is a graphical display that simultaneously describes several important features of the data set, such as center, spread, departure from symmetry, and identification of observations that lie usually far from the bulk of the data (outliers).
6.4.2 Distribution II
What is a bell-shaped curve probability distribution?
How a log transformation can help make a relationship clear?
The log transformation can be used to make highly skewed distributions less skewed. This can be valuable both for making patterns in the data more interpretable and for helping to meet the assumptions of inferential statistics.
Data Patterns or Empirical distribution
Graphic displays are useful for seeing patterns in data. Patterns in data are commonly described in terms of: center, spread, shape, and unusual features.
Some common distributions have special descriptive labels, such as symmetric, bell-shaped, skewed, etc.
- Graphically, the center of a distribution is located at the median of the distribution. This is the point in a graphic display where about half of the observations are on either side.
- The spread of a distribution refers to the variability of the data. If the observations cover a wide range, the spread is larger. If the observations are clustered around a single value, the spread is smaller.
- The shape of a distribution is described by the following characteristics: Symmetry, Number of peaks, Skewness, Uniform.
- Unusual Features are: gaps and outliers.