Statistics Chapter 2: Displaying Categorical Data

Distribution of a Variable

Tells us what values the variable takes and how often it takes each value

Frequency table

Shows the number of individuals having each data value

Relative Frequency table

Shows the proportion or percentage of individuals having each data value

What helps to summarize a variable’s distribution?

Both frequency tables and relative frequency tables

How to start frequency and relative frequency tables?

Tally the number of times the variable takes each value

Bar Chart

Shows each category as a bar

What part of a bar chart shows the category frequencies/relative frequencies?

The heights of the bar

Are bar charts or pie charts more flexible?

Bar charts

Pie Chart

Shows each category as a sector of a circle

Use a ___ ___ when you want to emphasize each category’s relation to the whole.

Pie chart

When are pie charts appropriate?

When data are categorical and all individuals have exactly one value

Two-Way Table

A table of frequencies (or relative frequencies) that summarizes the relationship between two categorical variables for some group of individuals

Be sure to use _____ instead of _____ when analyzing data of two categorical variables.

Relative frequencies; Frequencies

Why are relative frequencies better for comparing two categorical variables than frequencies?

It makes it easier to compare groups of different sizes

Side-by-Side Bar Chart

Displays the distribution of a categorical variable for each value of another categorical variable

Segmented Bar Chart

Displays the distribution of a categorical variable as portions (segments) of a rectangle, with the area of each segment proportional to the percentage of individuals in the corresponding category

When is there an association between two categorical variables?

If knowing the value of one variable helps to predict the value of another

_____ does not imply causation.

Association

Dotplot

shows each data value as a dot above its location on a number line

Roughly Symmetric

A distribution in which the right side of the graph is approximately a mirror image of the left side

Skewed to the Right

A distribution in which the right side of the graph is much longer than the left side

If distributions are about the same for all points, we can describe the shape as _____

Approximately Uniform

How do you characterize graphs with a single peak? A double peak? More than two peaks?

Unimodal, bimodal, multimodal

What are 2 steps to describe the distribution of a quantitative variable?

1. Look at its shape, center, and variability

2. Look for departures such as outliers

What to use to describe the center of a data set?

The median

What to use to describe the variability of a data set?

The minimum and maximum values of the data

When describing the distribution of a quantitative variable, look for the ____ ____ and for ____ ____ from that pattern.

overall pattern; clear departures

Stemplot

Shows each data value separated into two parts: a Stem, which consists of the left most digit(s), and a Leaf, the final digit

How are stems ordered in a stemplot?

From least to greatest and arranged in a vertical column

How are leaves ordered in a stemplot?

Arranged in increasing order out from the stems

What are 4 steps to make a Stemplot?

1. Make stems

2. Add leaves

3. Order leaves

4. Add a key

Should you add all stems in the stemplot, even if there’s no data value for a particular stem?

Yes

When splitting stems, make sure that an _____ _____ of possible leaf digits are assigned to each stem.

equal number

Histogram

Shows each interval as a bar and groups nearby values together

What is the minimum number of intervals used for a Histogram?

Five

What are 5 steps to making a Histogram?

1. Choose equal-width intervals

2. Make a table

3. Draw and label the axes

4. Scale the axes

5. Draw bars

When making a Histogram, the left endpoint of an interval is _____ and the right endpoint is _____.

included; excluded

True/False: The choice of intervals in a Histogram can affect the appearance of a distribution

True

What is the difference between a Histogram and a Bar Chart?

A histogram displays the distribution of quantitative variables

A bar chart displays the distribution of categorical variables

True/False: Dotplots, stemplots, and histograms show every individual value in a set of quantitative data

False

Scatterplot

Shows the relationship between two quantitative variables measured on the same individuals

On a Scatterplot, on which axis does the Explanatory Variable go?

On the horizontal or x-axis

What are the 4 steps to describing a Scatterplot?

1. Direction - it can a show positive, negative, or no association

2. Form - it can show a linear form or nonlinear form

3. Strength - it can show a weak, moderate, or a strong association

4. Outliers - individual points that fall outside the overall pattern of the relationship

Timeplot

A Scatterplot with consecutive points connected by a line segment

What does a timeplot show?

It shows how a single quantitative variable changes over time