Elementary Statistics

1
Elementary Statistics

• Chapter 4

2
Definitions

• A unit is the item or object we observe. When the
  object is a person, we refer to the unit as a
  subject.

• An observation is the information or
  characteristic recorded for one unit.

• A characteristic that can vary from unit to unit
  is called a variable.

• A collection of observations on one or more
  variables is called a data set.

3
Think About It

• Pg. 186

4
Qualitative Variables

• Qualitative variables are those that classify the
  units into categories. The categories may or may
  not have a natural ordering. Qualitative
  variables are also called categorical variables.

5
Quantitative Variables

• Quantitative variables have numerical values that
  are measurements (length, weight, etc.) or
  counts. Arithmetic operations on such numerical
  values do have meaning. We further distinguish
  quantitative variables based on whether or not
  the values fall on a continuum.

6
Quantitative Variables

• A discrete variable is one for which you can
  count the number of possible values. A
  continuous variable can take on any value within
  a given interval.

7
Lets Do It!

• Pg. 187, 4.1

8
Distribution

• The distribution of a variable provides the
  possible values that a variable can take on and
  how often these possible values occur. The
  distribution of a variable shows the pattern of
  variation of the variable.

9
Two-way Frequency Table

• Ages vs Gender of a statistics class.

10
Two-way Frequency Table

• The marginal distribution of the row variable is
  found by computing the percentage of each row
  total based on the grand total.

• The marginal distribution of the column variable
  is found by computing the percentage of each
  column total based on the grand total.

11
Two-way Frequency Table

• The conditional distribution of the row variable,
  given the column variable, is found by expressing
  the entries in the original table as percentages
  of the column totals.

12
Two-way Frequency Table

• The conditional distribution of the column
  variable, given the row variable, is found by
  expressing the entries in the original table as
  percentages of the row totals.

13
Shapes of Distributions

• Symmetric - the distribution can be divided into
  two parts around a central value, each part is
  the reflection of the other.

• Unimodal - the distribution has a single peak
  that shows the most common value(s) in the data.

14
Shapes of Distributions

• Bimodal - the distribution has two peaks. This
  often results when two populations are being
  sampled.

• Uniform - the possible values appear with equal
  frequency.

• Skewed - one side of the distribution is
  stretched out longer than the other side. The
  direction of the skewness is the direction of the
  longer side.