# 9.1 – Numerical Data

## Key Terms

• Bar Graph – A graphical display that uses bars to show frequencies of categorical, or qualitative, data.
• Categorical Data – Data that can be described only with words.
• Classes – Numerical intervals used to group data.
• Comparative Dot Plot – A chart that uses stacked dots to represent frequency counts for two or more sets of data for the purpose of comparison.
• Comparative Stem-and-Leaf Plot – A table that is used to organize and compare two similar data sets. The table has three columns. The tens digit, or stem, will be the center column.
• The left column represents the leaves of one set of data, and the right column represents the leaves of the second set of data.
• They share a stem.
• Continuous Data – Data for which there are an infinite number of possible values.
• Discrete Data – Data for which there are a finite number of possible values.
• Dot Plot – A chart that uses stacked dots to represent frequency counts.
• Frequency Distribution – The arrangement of a set of data according to frequency of occurrence.
• Frequency Table – A table that shows each data element and the number of times that it occurs (i.e., its frequency) in the data set.
• Histogram – A graph that uses bars to show how many data values are in each numerical range.
• Numerical Data – Data that can be described with numbers.
• Repeating Stem – A number in the left column of a stem-and-leaf plot that has more than one corresponding number (or “leaf”) in the right column.
• Stem-and-Leaf Plot – A table used to organize data values in which the tens digits and the ones digits of the data values are separated into columns.
• Stem-and-leaf plots are also called stemplots.
• Univariate Data – Data that comprise a set of values for a single variable.

## Notes

Numerical Data Categorical Data
• Favorite colors and college majors are examples of categorical data, or data that can only be described with words or titles.
• Temperature and cost are examples of numerical data, or data that can only be described with numbers.
Discrete Data Continuous Data
• Discrete data are data for which there are finite number of possible values.
• Examples of discrete data
• Rides at Six Flags
• Algebra 1 Students in 3rd Period
• Pages in a Book
• Bagels in a bag
• Continuous data are data for which there are an infinite number of possible values.
• Examples of continuous data
• Weight
• Length
• Temperature
• Distance
• Area
Univariate Data
• In the word univariate, uni means one, and variate sounds like variable.
• Univariate data are data that represent a single variable.
• Some possible ways that univariate numerical data can be represented:
1. Dot plots
2. Histograms
3. Stem-and-leaf plots
4. Frequency tables
Dot Plots
• Dot plots are plots used to display frequency counts (or the number of times a variable occurs).
• Stacking two dot plots with different data sets on top of each other will create a comparative dot plot.

• Stacking the dot plots of these data sets on top of each other creates the comparative dot plot.

Histograms
• Histograms are only used for numerical data.
• It shows numerical values that are in classes.
• With a histogram, the height of each bar represents the number of occurrences in that class.
• The class intervals are shown on the horizontal axis and the frequencies are shown on the vertical axis.
• Each bar touches the bars to its left and right.
• There are no gaps between the bars, or classes.
• A good histogram will have:
1. Between 5 and 15 classes.
2. No overlap between classes.
3. Equal class sizes.

• You can also use a histogram to display a relative frequency distribution.
• For a relative frequency histogram, the largest number you ever need on the vertical axis is 1, because you cannot have more than 100% of the data in any one class.

• Histograms are NOT bar graphs!
• A bar graph is used for categorical data.
• The bars in a bar graph don’t touch each other.
• The horizontal axis of a bar graph shows categories instead of classes.
• The vertical axis shows the number of occurrences for each category.
Stem and Leaf Plots
• The downside of using a histogram is that you can’t see all of the individual data points.
• If you need to see each data value, a stem-and-leaf plot  is useful.
• Stem-and-leaf plots can sometimes hide certain patterns, so it can be useful to make stem-and-leaf plots with repeating stems.
• In a stem-and-leaf plot, values are grouped by similar “stems,” and each “leaf” is shown separately.
• Therefore all of the data are shown on the chart itself.

• The first step of building a stem-and-leaf plot is to arrange the values from least to greatest.
• To create a comparative stem-and-leaf plot, you need three columns.
• The tens digits, or stem, will be in the center column.
• The left column represents the leaves of one set of data, and right column represents the leaves of the second set of data.
Frequency Tables
• A frequency table keeps track of how many times each value occurs. Instead of listing every piece of data, it provides you with a more clear understanding of the frequency distribution  for the data set.
• Sets of Data: Large vs Small
• A list shows all the values in your data set. It is best used with small sets of data
• A frequency table keeps track of how many times each value occurs. It helps organize larger sets of data.
• Classes
• Sometimes frequency tables group data into classes  instead of listing the frequency of every value.
• The last value in one class should not be the same as the first value in the next class.
• You should choose the class size that is most useful in helping you understand and analyze the data.
• To create a frequency table for a given set of univariate data:
• Draw a table with two columns.
• One column lists the various categories, and the other column lists the frequencies of each.