Use the applet Standard Deviation to study the effect that multiplying or dividing each number in a data set by the same number has on the standard deviation. Begin by setting appropriate limits and plotting the given data on the number line provided in the applet.
0 1 1 1 2 2 3 4
a. Record the standard deviation. Then multiply each data item by 2, plot the new data items, and record the standard deviation. Repeat the process, first multiplying each of the original data items by 3 and then by 4. Describe what happens to the standard deviation as the data items are multiplied by ever higher numbers. Divide each standard deviation by the standard deviation of the original data set. Do you see a pattern? Explain.
b. Divide each of the original data items by 2, plot the new data, and record the standard deviation. Repeat the process, first dividing each of the original data items by 3 and then by 4. Describe what happens to the standard deviation as the data items are divided by ever higher numbers. Divide each standard deviation by the standard deviation of the original data set. Do you see a pattern? Explain.
c. Using your results from parts a and b, describe what happens to the standard deviation of a data set when each of the data items in the set is multiplied or divided by a fixed number n. Experiment by repeating parts a and b for other data sets if you need to.