chapter 1.4. variable: any characteristic whose value may change from one individual to another...
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Chapter 1.4
Variable:
• any characteristic whose value may change from one individual to another
Data:
• observations on single variable or simultaneously on two or more variables
Types of variables
Categorical variables
• or qualitative
• identifies basic differentiating characteristics of the population
Numerical variables• or quantitative
• observations or measurements take on numerical values
• makes sense to average these values
• two types - discrete & continuous
Classification by the number of variables
• Univariate - data that describes a single characteristic of the population
• Bivariate - data that describes two characteristics of the population
• Multivariate - data that describes more than two characteristics (beyond the scope of this course
Identify the following:
• gender• age• hair color• smoker • systolic blood
pressure• number of girls in
class
• categorical• numerical• categorical• categorical• numerical• numerical
Categorical Data
Frequency
• the number of times the category appears in the data set
Frequency Distribution
• a table that displays the possible categories along with the associated frequencies or relative frequencies
Relative Frequency• The fraction or proportion of
the time that the category appears in the data set;
frequency
# of observations in the data set
Relative Frequency
• percent displayed as a decimal
Relative Frequency Distribution
• a table that includes relative frequencies
Table 4. Life of AA batteries, in minutes
Battery life, minutes (x)
Frequency (f)Relative frequency
Percent frequency
360–369 2 0.07 7
370–379 3 0.10 10
380–389 5 0.17 17
390–399 7 0.23 23
400–409 5 0.17 17
410–419 4 0.13 13
420–429 3 0.10 10
430–439 1 0.03 3
Total 30 1.00 100
Life of AA batteries, in minutes
Bar Graphs• Provides a visual representation
of the information from a frequency distribution where the area of each bar is proportional to the corresponding frequency
• Look for frequently and infrequently occurring categories
BAR GRAPHS
• Step 1: Label your axes of the graph. Draw a set of axes. Label you horizontal axis with your type that your categories fit in to. Title your graph.
• Step 2: Scale your axes. Use the counts in each category to help you scale your vertical axis. Write the category names at equally spaced intervals beneath the horizontal axis.
• Step 3: Draw a vertical bar above each category name to a height that corresponds to the count in each category.
Numerical Data
Discrete (numerical)
• listable set of values
• usually counts of items
Continuous (numerical)
• data can take on any values in the domain of the variable
• usually measurements of something
DOT PLOT• Use for small data sets• Each observation is
represented by a dot; dots are stacked vertically
• Look for: spread of data, nature of distribution of data, unusual data values
DOT PLOTS• Step 1: Label your axis and title your
graph. Draw a horizontal line and label it with the variable. Title your graph
• Step 2: Scale the axis based on the values of the variable
• Step 3:Mark a dot above the number on the horizontal axis corresponding to each data value.
The number of goals scored by each team in the first round of the California Southern Section Division V high school
soccer playoffs is shown in the following table.
5 0 1 0 7 2 1 0 40 3 0 2 0 3 1 5 0 3 0 1 0 1 0 2 0 3