Lesson 2 Homework Practice Measures Of Variability
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Measures of variability. Values that show how much the quantitative data varies.Also known as measures of spread. Note: This is not taught during this lesson, butwill be addressed as part of Lesson 4.
Students should complete the Mr. Jones Mile Rule Times handout (LMR_2.3) for homework. Theycan practice finding the mean of distributions by determining a balancing point for the data. Answersto the handout are below. Note: The mean values in part (3) do NOT need to be exact. LMR_2.3
In addition to figuring out the measures of central tendency, we may need to summarize the amount of variability we have in our distribution. In other words, we need to determine if the observations tend to cluster together or if they tend to be spread out. Consider the following example:
Both of these samples have identical means (5) and an identical number of observations (n = 5), but the amount of variation between the two samples differs considerably. Sample 2 has no variability (all scores are exactly the same), whereas Sample 1 has relatively more (one case varies substantially from the other four). In this course, we will be going over four measures of variability: the range, the inter-quartile range (IQR), the variance and the standard deviation.
The horizontal line that runs across the center of the box indicates where the median falls. Additionally, boxplots display two common measures of the variability or spread in a data set: the range and the IQR. If you are interested in the spread of all the data, it is represented on a boxplot by the vertical distance between the smallest value and the largest value, including any outliers. The middle half of a data set falls within the interquartile range. In a boxplot, the interquartile range is represented by the width of the box (Q3 minus Q1).
To have SPSS calculate measures of central tendency and variability for you, click "Analyze," "Descriptive Statistics," then "Frequencies." Measures of central tendency and variability can also be calculated by clicking on either "Descriptives" or "Explore," but "Frequencies" gives you more control and has the most helpful options to choose from. The dialog box that opens should be pretty familiar to you by now. As you did when calculating frequency tables, move the variables for which you would like to calculate measures of central tendency and variability into the right side of the box. You can uncheck the box marked "Display frequency tables" if you'd rather not see any tables and would prefer to see only the statistics. Then click the button on the right labeled "Statistics." From the Dialog box that opens you may select as many statistics as you would like (Note: SPSS uses the term "Dispersion" rather than "Variability," but the two words are synonymous). Also, please be aware that SPSS will calculate statistics for any variable regardless of level of measurement. It will, for example, calculate a mean for race or gender even though that makes no sense whatsoever. Male + male + female/3 = 0.66? Totally illogical. This is one of the many circumstances in which you will have to be smarter than the data analysis package you are using. Just because SPSS will let you do something doesn't necessarily mean it's a good idea.
When calculating measures of variability, it is sometimes helpful to include a box plot. To do so, click on "Graphs," then "Legacy Dialogs" and select "Box Plot." As was the case with the graphs you created in the previous chapter, you'll have several options from which to choose. Generally speaking, you'll want one boxplot for each variable, so choose "Summaries of Separate Variables." Move the variables that you would like to see displayed as box plots to the empty box on the right and click OK. Should you desire to edit your boxplots, you can do so in much the same way you did the graphs in Chapter 2. Here's a video walkthrough:
Next, consider two common measures of the variability in \(\pi\).The variance in \(\pi\) roughly measures the typical or expected squared distance of possible \(\pi\) values from their mean:
Proportionally increase or decrease the number of questions in the assignment. This is very useful when planning a lesson. You can create a few questions to use as examples, and then scale up the number of question to create a homework assignment. The questions on the homework will be completely new, yet follow precisely from the lesson--and you don't need to design the questions again. 2b1af7f3a8