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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 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.

 

Alg1B - 9.1 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.
Alg1B - 9.1 Histogram
 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.
Alg1B - 9.1 Stem Leaf
 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.
Alg1B - 9.1 Frequency Table

 

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