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Visualizing Variation Exercise

(Applets and parts of this exercise are from The Shodor Education Foundation, Inc. © Copyright. For more information, visit )

Raw data and descriptive stats:

Go to . On the first screen you need not enter any thing here, so hit the “Proceed” button. Click on mean, median, range and deviation, then hit the “Proceed” button (click on the “Learner” tab if you need to review these terms). Create a data set by sliding the bars for each of the five data points.

• What is the greatest deviation value (variation) you can create? What is the least?

• Set the number of subjects (“plants”) to be three. Find several different settings of measurements for which mean and median are different. Now find several different settings when mean and median are about the same. What happens to standard deviation (variation) as the difference between mean and median decrease?

• Set the number of subjects (“plants”) to be 10. Set 9 of the measurements to be the same, and the last one different by many points (e.g., set nine measurements to 3 and the tenth to 50). What are the mean and the median? Which one represents the data better?

• Is it possible to create two data sets with the similar standard deviations but different means?

Frequency histograms:

A collection of numbers in a data set can be effectively visualized by tabulating and plotting the number (frequency) of data points that fall within each of several categories (i.e, within assigned intervals). Go to . Click on areas within the axes to add points (i.e. the frequency of counts) to any of the intervals (i.e. categories or “bins”) along the horizontal axis.

• Construct a graph for which mean and median are different. Now find several different settings when mean and median are about the same. Describe or draw these graphs.

• Speculate what happens to standard deviation (variation) as the difference between mean and median decrease?

Normal Distribution:



This applet lets you see how the results of an experiment with a lot of trials might look. Experiment with moving the standard deviation lines to change the shape of the graph.

• How are the standard deviation and the shape of the graph related?

• Does the area below the curve seem to change when the standard deviation gets bigger or smaller?

• Create a histogram with 100 trials. Experiment with the bin size. Does the histogram look like it fits the curve well? Does it depend on bin size? Does it help more to have bigger or smaller bins?

• Try the same experiment with 1000 trials, then 5000 (set bin size relatively small). Is the normal curve approximation more accurate for large or small samples?

• If you had only ten trials, do you think you would be likely to get a nice, smooth normal distribution?

Comparing Variation:

The following figures are from you lab handout. The means in all 3 graphs in Figure 6 are the same.

|[pic] |[pic] |

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|Figure 5. The t-test |Figure 6. t-test comparison of distributions |

• If t-tests were run to determine whether the two groups were significantly different than one another, which data set would be more likely to be significantly different (Low, Medium, or High variability)? Explain why.

• In which data set would the difference between the means most likely be due to chance (Low, Medium, or High variability)? Explain why.

|[pic] |[pic] |

Figure 15. The role of error bars in estimating differences in treatment groups

The means in both graphs in Figure 15 are the same.

• If t-tests were run to determine whether the two groups (forest versus field) were significantly different than one another, which data set would be more likely to be significantly different (the graph on the left or the one on the right)? In which data set would the difference between the means most likely be due to chance (the graph on the left or the one on the right)?

• Which type of graphs convey more information about the actual data set (a histogram from Figure 6 or a bar graph from Figure 15)? Explain why.

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