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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 StemandLeaf 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 stemandleaf plot that has more than one corresponding number (or “leaf”) in the right column.
 StemandLeaf 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.
 Stemandleaf 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:
 Dot plots
 Histograms
 Stemandleaf plots
 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:
 Between 5 and 15 classes.
 No overlap between classes.
 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 stemandleaf plot is useful.
 Stemandleaf plots can sometimes hide certain patterns, so it can be useful to make stemandleaf plots with repeating stems.
 In a stemandleaf 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 stemandleaf plot is to arrange the values from least to greatest.
 To create a comparative stemandleaf 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.


Important!
Practice (Apex Study 9.1)
 Try practice problems on Pgs 8, 14, 19
 Mandatory: write and answer problems on Pgs 15, 20
 1 Quiz
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