DUE 5PM EST

· DoW #4: How Do Students Value Statistics? DATA ATTACHED

An instructor wanted to answer the question, “How do my students value statistics?”

She collected data on the variable, “opinion on value of statistics” by asking students in six classes to rate their opinion of statistics on a scale of 1 to 10, where “1” means little or no value and “10” means highly valuable. The data is provided in histograms

· Investigation 1: Seeing the Spread

Spread refers to the variation of the distribution for a variable. You already know two simple measures of spread:

· Range: The simplest measure of spread is the range: the difference between the maximum and minimum values of the distribution. In essence, the range tells us the width of the distribution – how many different values the variable takes on, but it does not tell us how the data falls within that range. For instance, consider a class where every student scores 80% on a test, except for one student who scores 10%. This class’s scores are not very variable – nearly every student scored 80%; yet the range would be 70%, suggesting the data is more variable than it really is.

· Interquartile Range (IQR): The IQR was introduced in Week 3. It is the difference between the third quartile and the first quartile. The IQR measures the width of the middle 50% of the distribution – how different the middle values are from each other. Another way of thinking about it is as a measure of variation around the median. The smaller the IQR, the better the median represents the middle 50% of the data. IQR is a little more focused than the range, in that it filters out the extremes of the data (the highs and the lows). However, in doing so, it ignores 50% of the data. Smaller IQRs imply less variation in the distribution. However, it is possible for the upper and lower 25% of the data to be wide-spread. For instance, consider a class where 75% of the students score 90% on a test and the remaining 25% of the students score 50%. In this case, the IQR is 0, suggesting little variation in the distribution of the scores from the median score of 90%; yet 25% of the students did not pass this test.

The appeal of both of these measures is their simplicity. Each is a simple difference of values and can be easily estimated visually on a histogram or box plot. They serve as good initial measures for comparison, used in conjunction with visual comparisons of the key features of the distribution. In Activity A, we look more intuitively at the spread in DoW #4, and in Activity B, we introduce "deviations from the mean" as another way of measuring spread.

· Inv 1, Activity A: The Spread of DoW #4

Exercise A1: Look at the histograms presented in DoW #4., describe the spread of the distributions. Some things to consider as you do this:

· Class G and Class I have the same range. Would you say their variation is the same? Why or why not?

· Compare Class F and Class J. Which would you say has the greater variation? Why?

· Overall, which class(es) appear to show the least variation? The greatest? Why?

Exercise A2: Below are the boxplots of the classes in DoW #4. Match the histograms in DoW #4 to their corresponding boxplots. *** Complete Exercises A1 and A2 before moving on. DoW #4

Exercise A3: The file DOW4.xlsx contains the data for DoW #4. Check your work In Exercise A2 by creating the box plots for these classes. Reflect in your journal: What features of the histograms are easily matched to the box plots? Which features of a histogram are lost in a box plot? Exercise A4: Calculate the range and IQR for the six classes in DoW #4. Try to do this from the graphs. You can check your answers using a calculator or spreadsheet. Also, comment on whether or not there are any outliers for the distribution by the IQR method. (Remember, you can see outliers on the modified box plots in Fathom.) Record your findings in a table like the one below. Here's a template. Note: Some columns are for later activities...

Class	Range	IQR	Outliers? IQR Method	MAD	SD	Outliers? SD Method
C
F
G
H
I
J

Exercise A5:

· Which class has the largest range? largest IQR?

· Which class has the smallest range? smallest IQR?

· Compare these statistics to your first impressions of the variation in DoW #4, from Exercise A1.

Exercise A6: Reflect on your work in Activity A. In 250 words, summarize your thoughts on the variation we see in the six classes in DoW #4. Consider the following as you compose your thoughts thus far:

· Which class(es) do you think show the most variation? The least?

· For which classes is it less clear to you how their variation compares to the other classes?

· Which tools do you think best allow you see the variation in the data set (histogram, boxplot, range, IQR)?

· What doesn’t the range tell you about the spread of a distribution? What doesn’t the IQR tell you about the spread of a distribution?

· What questions or further thoughts do you have about DoW #4 or measuring spread?

· Exercise A7 (E3): In this week’s work, we have analyzed the spread of DoW #4 in a variety of ways. In this DoW, we are trying to answer the question, “How do my students value statistics?”

In which classes is the answer most clear? How do measures of spread help you answer the question?