Presenting & Describing Quantitative Data

What is statistics?

• The science of collecting, organizing, and interpreting numerical facts (data) with the goal of gaining understanding about a problem.

• Always relate calculations back to the problem at hand as numbers alone are not meaningful.

• Requires thinking and judgment about data.

Variables

• A variable is a characteristic of an individual, or object of interest (i.e.- person, plant, animal)

Distributions

The distribution of a variable tells us what values of the variable were observed and how often.

• Ex: Consider 10 rose bushes in a garden• What colors are represented?

• How many of each color?

Types of Variables

Categorical Quantitative- Value falls into one oftwo or more groups, or categories.

- Ex. Blood type, hair color

- Takes on numerical values- Mathematical operations (such asaveraging) make sense

- Ex. Height, age, number of credit cards owned

It makes sense to talk about the average height (quantitative) of the students in the class, but not the average blood type (categorical).

Displaying Categorical Data with Graphs

For a categorical variable, the distribution lists the categoriesand the count or percent of individuals who fall into each one.

• Bar graphs

– each category is represented by a bar

• Pie charts

– The slices must represent parts of one whole

• Line Graphs

– Each category is represented by

a point

Displaying Quantitative Data with Graphs

• Dot Plot– shows a dot for each observation

placed above its value on a number line

• Stem-and-Leaf Plot– portrays the individual observations

• Histogram– uses bars to portray the data

Displaying Quantitative Data with Graphs

• Box & Whisker Plot– uses quartiles to portray data

• Scatter Plot– shows the relationship between 2

numeric variables

Which Graph Should I Use?

• Dot-plot & Stem-and-leaf plot:– More useful for small data

sets– You can see individual data

values

• Box and Whisker Plot & Histogram– More useful for large data sets– Most compact display– More flexibility in defining

intervals

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Really Important Difference to Understand

Histograms

• Numerical version of bar graph

– The range of values a variable can take on is divided into equal size intervals, called “bins”.

– Histogram shows number of data points (observations) that fall into each bin.

– Choosing the correct bin size is judgment call.

• Too large?

• Too small?

HistogramTest 1 scores for 10 statistics students

Test Score

#o

f St

ud

ents

10 bins

Student Score1 752 993 794 715 666 827 898 09 5310 73

What if we change the bin size?

Test Score

#o

f St

ud

ents

4 bins

Your Assignment Part 1

• Create a histogram of the “Actual Test Score” data from the CPM classes.– What is the variable here?– What is the range of this variable?– Which axis does the variable go on?– What does the other axis measure?– Decide on a reasonable bin size as a table.