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9.1 – Numerical Data
- 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.
| Numerical 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 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
- 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
- Stem-and-leaf 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 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 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.
- 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.
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