In order to ensure that customer inquiries are being handled efficiently at a he

Question

In order to ensure that customer inquiries are being handled efficiently at a help desk call center, the center wants to estimate how much time, on average, their staff spend on the phone with a customer. A sample of 50 randomly selected calls yielded a sample average of 7.7 minutes and a sample standard deviation of 3.2 minutes. The call duration distribution, however, is highly skewed to the right.

Suggest a plausible reason for the call duration distribution to be right skewed.

Why can one still make an inference about the average call time even though the distribution is skewed right?

Explanation / Answer

The call duration being right skewed(positively skewed) means that the mean duration of the calls of the group is greater than the median. It means that either the duration of calls of people was more than expected and/or for some people it was more than expected. This can also be because of the presence of outliers ie some values which are very large as compared to the average of 7.7 so it affects the mean but not the median and so mean>median and thus we have a right skewed distribution.

Even though the average call time may be influenced by outliers we can still make an inference about it since we have a large data set here(50 values). We can use the median but in some cases, like conducting hypothesis tests whether a particular value is the true mean, higher or lower than mean we need the mean value and standard deviation to convert to a normal approximation. These can't be compared using a median. Since the standard deviation gives the amount of variability of values from the mean, knowing this we can make inferences about the average call time.

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