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The Hurricane Database (HURDAT) has records since 1851 on the most destructive hurricanes. According the HURDAT,...

The Hurricane Database (HURDAT) has records since 1851 on the most destructive hurricanes. According the HURDAT, hurricane Mitch in 1998 had the highest sustained wind speed of 180mph. Suppose a typo is made when analyzing the top 20 hurricanes of all time in terms of sustained wind speed and this data point is put into the data set as 18 rather than 180. What effect would this have on the mean and standard deviation of the analysis?

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Answer #1

There are 20 values in the data of hurricanes that is being summarized. Also given is that for one year 1998, the speed is entered as 18 instead of 180. Since the mean is the total divided by 20, the wrong total will be 180-18=162 less in the total. Hence, the calculated mean using 18 will be lesser by 162/20=8.1.  

For Sd, we are adding up the squared deviation from the mean. Since the mean is lesser by a quantity 8.1 and the deviations will be more and hence the variance will be increased and also the SD.

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