Determine (by hand) the best measure of central tendency for the amount of snowf

Question

Determine (by hand) the best measure of central tendency for the amount of snowfall.

The following data represents the amount of snowfall (in inches) received by Squaw Valley from the 1996 season the the 2005 season.

399   542   347   381   400   289

358   439   602   661

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Suppose the observation of 661 inches was incorrectly recorded at 1661 inches. Compute the mean and median with this change. What did you notice? What property of the median is illustrated here??

Explanation / Answer

Ordering the data,

289
347
358
381
399
400
439
542
602
661

Hence, the mean is

Mean = Sum(x)/n = 4418/10 = 441.8

While the median is the average of the middle terms,

Median = (399+400)/2 = 399.5

**************
Now, when the error is made, the new data set is

289
347
358
381
399
400
439
542
602
1661

Hence, the mean is

Mean = Sum(x)/n = 5418/10 = 541.8

While the median is the average of the middle terms,

Median = (399+400)/2 = 399.5

***************

As we can see, the mean changed a lot, but the median remained the same, as only the order matters to the median, not the individual values. This shows the robustness of the median.

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