Categorical and Quantitative variables Example

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Categorical and Quantitative variables Example

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Categorical and Quantitative variables Example

Categorical Type of pet owned (cat, fish, dog) Favorite book, song
Gender Model of car

Numbers of pets owned (2 pets)
Numbers of books in the library (100 books)
Weight in pounds
Bank account balance

Gender is a categorical variable but looks like quantitative. Because arithmetic operations doesn’t make sense for it.

Example 1.3 Here are data on the percents of first-year students who plan to major in several areas:

Field of study Arts Social science Economics Engineering Business Other majors Total

Percent of students 13.2 18.3 16.9 12.1 23.7 15,7 99.9

Why not 100%? The exact percents would add to 100, but each percent is rounded to the nearest tenth. This is roundoff error.

A pie chart must include all the categories that make up a whole
Arts Social science Economics Engineering Business Other

The bar heights show the category counts or percents (the bar in alphabetical order).
25 20 15 10
5 0

In order of height
25 20 15 10
5 0

Example 1.4 (homework 1.4 in book) The Higher Education Research Institute’s Freshman Survey reports the following data on the sources students use to pay for college expenses.

Source for college expenses Family resources Student resources Aid – not to be repaid Aid – to be repaid Other

Students 78,4% 64,3% 73,4% 53,1% 7,1%

Why it is not correct to use a pie chart?

But we can build a bar graph for these data











Family Student Aid - not Aid - to be Other

resources resources to be



—  Appropriate for quantitative variables that take
many values and/or large datasets.
—  Divide the possible values into classes (equal
—  Count how many observations fall into each
interval (may change to percents).
—  Draw picture representing the distribution―bar
heights are equivalent to the number (percent) of observations in each interval.

Interpreting Histograms
—  In any graph of data, look for the overall
pattern and for striking deviations from that pattern.
—  You can describe the overall pattern by its
shape, center, and variability. You will sometimes see variability referred to as spread.
—  An important kind of deviation is an outlier, an
individual that falls outside the overall pattern.

Describing Distributions
—  A distribution is symmetric if the right and left sides of the
graph are approximately mirror images of each other.
—  A distribution is skewed to the right (right-skewed) if the
right side of the graph (containing the half of the observations with larger values) is much longer than the left side.
—  It is skewed to the left (left-skewed) if the left side of the
graph is much longer than the right side.