# Categorical and Quantitative variables Example

## Transcript Of Categorical and Quantitative variables Example

Categorical and Quantitative variables Example

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

Gender Model of car

Quantitative

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

90

80

70

60

50

40

30

20

10

0

Family Student Aid - not Aid - to be Other

resources resources to be

repaid

repaid

Histograms

Appropriate for quantitative variables that take

many values and/or large datasets.

Divide the possible values into classes (equal

widths).

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

EXAMINING A HISTOGRAM

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.

Symmetric

Skewed-left

Skewed-right

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

Gender Model of car

Quantitative

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

90

80

70

60

50

40

30

20

10

0

Family Student Aid - not Aid - to be Other

resources resources to be

repaid

repaid

Histograms

Appropriate for quantitative variables that take

many values and/or large datasets.

Divide the possible values into classes (equal

widths).

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

EXAMINING A HISTOGRAM

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.

Symmetric

Skewed-left

Skewed-right