So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The...
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![Page 1: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/1.jpg)
So What Do We Know?
• Variables can be classified as qualitative/categorical or quantitative.
• The context of the data we work with is very important. Always think about the “Five W’s”—Who, What, When, Where, Why (and How)—when examining a set of data.
![Page 2: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/2.jpg)
The Three Rules of Data Analysis
• The three rules of data analysis won’t be difficult to remember:
1.Make a picture—things may be revealed that are not obvious in the raw data. These will be things to think about.
2.Make a picture—important features of and patterns in the data will show up.
3.Make a picture—the best way to tell others about your data is with a well-chosen picture.
![Page 3: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/3.jpg)
Qualitative Data :: Making Piles
• We can “pile” the data by counting the number of data values in each category of interest.
• We can organize these counts into a frequency table, which records the totals & category names.
• A relative frequency table is similar, but gives the percentages (instead of counts) for each category.
![Page 4: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/4.jpg)
What Do Frequency Tables Tell Us?
• Frequency tables and relative frequency tables describe the distribution of a categorical variable because they name the possible categories and tell how frequently each occurs.
• Graphs … Pie Charts & Bar Graphs (software)
![Page 5: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/5.jpg)
• A contingency table allows us to look at two qualitative variables together.
• Note the totals in the margins of the table. Each set of totals gives us the marginal distribution of the respective variable.
![Page 6: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/6.jpg)
So What Do We Know?
• Qualitative variables can be summarized in frequency or relative frequency tables.
• Categorical variables can be displayed with bar graphs and/or pie charts.
• A contingency table summarizes two variables at a time. From a contingency table we can find the marginal distribution for each variable or the conditional distribution for one variable conditioned on the other variable.
![Page 7: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/7.jpg)
Displaying Quantitative Data
HISTOGRAMS• First, slice up the entire span of values covered by the
quantitative variable into equal-width piles called classes/bins. “selection = art form”
• The bins and the counts in each bin give the distribution of the quantitative variable.
• One graphical display of the distribution of a quantitative variable is called a histogram, which plots the bin counts as the heights of bars (like a bar graph).
• A relative frequency histogram displays the percentage of cases in each bin instead of the count.
![Page 8: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/8.jpg)
• Stem-and-leaf displays show the distribution of a quantitative variable, like histograms do, while preserving the individual values.
• Stem-and-leaf displays contain all the information found in a histogram.
![Page 9: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/9.jpg)
• First, cut each data value into leading digits (“stems”) and trailing digits (“leaves”).
• Use the stems to label the bins.
• Use only one digit for each leaf if necessary either round or truncate the data values.
![Page 10: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/10.jpg)
• A dotplot is a simple display. It just places a dot for each case in the data.
![Page 11: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/11.jpg)
• When describing a distribution, make sure to always tell about L.O.S.S. !!!
Location/Center/Typical ValueOutliersSpread/DispersionShape/Distribution
![Page 12: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/12.jpg)
SHAPE
1. Symmetric
2. Skewed
3. Uniform or rectangular
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Symmetric
![Page 14: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/14.jpg)
SkewedRight-Tailed … Left-Tailed
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Uniform
![Page 16: So What Do We Know? Variables can be classified as qualitative/categorical or quantitative. The context of the data we work with is very important. Always.](https://reader035.fdocuments.in/reader035/viewer/2022062222/5697bf9e1a28abf838c9488d/html5/thumbnails/16.jpg)
So What Do We Know?
• Quantitative variables can be displayed using histograms, dotplots, and/or stem-and-leaf displays. These displays help us to see the distributions of the variables.
• Consider L.O.S.S. when looking at these displays! • Distributions can be classified as symmetric or
skewed (look at how the tails behave with respect to the rest of the distribution).