## Question 16:

1

No answer provided yet.The 10% trimmed mean of a data set is found by arranging the data in order, deleting the bottom 10% of the values and the top 10% of the values then calculating the mean of the remaining values. What advantages do you think that the trimmed mean has as compared to the mean?

Construct a data set for which the range is misleading as a measure of variation. Explain why the range is misleading and suggest an alternative measure of variation.
The question wants you to think about how a few values or even one value will skew the mean. For example, take a look at the following actual times from users attempting to complete a task in a software program (these values are the sample data loaded on the task time calculator page.)

43
52
36
37
136
38
37
39
42
39
52
You should notice the 136 time right away. The mean of this data set is 50 seconds, which is heavily influenced by the one outlying time of 136. The mean is used to express the "middle" or most likely value and in these situations, it bumps it up too high providing you with a bad estimate of the middle.

The trimmed mean, will provide a more stable estimate since these outliers wont skew the results. There are 11 values, so dropping 10% is liking dropping the max and min values. This then removed 136 and 36 to provide a trimmed mean of 42 seconds.

Using the same data set above, the range is 100 seconds. But once again, its because of the 136. Remove that value and the range is only 16 seconds, a huge difference. How about suggesting a Trimmed range? Take the values, rank them then drop the top 10% and bottom 10% just like as in the trimmed mean example. Then instead of taking the mean (sum/count) just express the maximum value minus the minimum value. In this case that value would be 15 seconds.