AAEC 4302 ADVANCED STATISTICAL METHODS IN AGRICULTURAL RESEARCH

1
AAEC 4302ADVANCED STATISTICAL METHODS IN
AGRICULTURAL RESEARCH

• Review of Familiar Topics
• Chapter 4 Frequency Distributions

2
Introduction

• Chapter 4 examines grouping and classification
  techniques for organizing and summarizing data on
  a given variable
• There are a few but important differences in the
  techniques applied to discrete vs. continuous
  variables

3
Discrete Data Variables

• Suppose that n observations are available on a
  discrete variable X that only takes m different
  values
• The n observations can be divided into m
  different groups within which all of the
  observations have exactly the same value

4
Discrete Data Variables

• These m different groups can be indexed by k, so
  that k 1,,m
• Example Family size variable on Table 2.2 (p.
  18)
• X ranges from 2 to 10, m 9 (k 1,,9), the
  100 observations can be arranged into nine
  groups, one for each family size value observed
  in the sample

5
Discrete Data Variables

• Table 4.1 (p. 63) is an example of a Frequency
  Table for the variable family size

6
Discrete Data Variables

• Figure 4.1 (p.64) is a conventional graph of the
  relative frequency distribution of the discrete
  variable family size (X) it is a graph of the
  value of fk for each value of Xk

7
Discrete Data Variables

• Since the relative frequency distribution
  implicitly orders the values of X, the median
  (Xmed) is easily found by examining the
  cumulative frequencies

8
Discrete Data Variables

• The mean can also be calculated from a frequency
  table instead of the raw data

9
Discrete Data Variables

• The standard deviation (SX) can also be
  calculated from a frequency table