250- 300 WORDS ONLY Focus on what you learned that made an impression, what may have surprised you, and what you found particularly beneficial and why. Specifically:
- What did you find that was really useful, or that challenged your thinking?
- What are you still mulling over?
- Was there anything that you may take back to your classroom?
- Is there anything you would like to have clarified?
THE Weekly Reflection will be graded on the following criteria for a total of 5 points:
Reflection is written in a clear and concise manner, making meaningful connections to the investigations & objectives of the week.
Reflection demonstrates the ability to push beyond the scope of the course, connecting to prior learning or experiences, questioning personal preconceptions or assumptions, and/or defining new modes of thinking.
NOTES TO USE: WHAT WE COVERED THIS WEEK
Introduction & Goals
The spread, or the variability, of a distribution is measured in many ways. In this week's investigations we will look in great detail at three measures of the spread of a distribution: IQR, Mean Average Deviation (MAD), and Standard Deviation (SD). These measures provide valuable tools for comparing distributions and evaluating the significance of their central measures.
Goals:
- Develop an understanding of mean as an indicator of fair allocation and as the "balancing point" of a set of data
- Explore deviations of data values from the mean
- Quantify variation in a distribution by calculating the Range, Interquartile Range (IQR), the Mean Absolute Deviation (MAD), or the Standard Deviation (SD) of the distribution
- Define outliers of data in terms of IQR (interquartile range) and number of deviations from the mean
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.