The data presented pertain to the number of minutes it took to change oil at one company location. The two descriptive statistics collected from these data were (a) mean and (b) standard deviation. Before commenting on these descriptive statistics, it would be appropriate to present the histogram of the data (see Figure 1 below).

There are several ways in which these data can be used to attract customers. First, given how busy customers are, one appropriate use for the data is to give customers insight into how long they can expect to wait,. Given the mean and standard deviation, an appropriate promise is ‘20 Minutes Or It’s Free!’ The reason that this promise can be made has to do with the normal distribution; although the oil change data do not demonstrate a perfectly Gaussian distribution, they probably offer a reliable idea of oil change durations at the company. In a normal distribution, 95% of the values lie within 2 standard deviations of the mean in either direction . Therefore, if the oil change data follow the normal distribution (which is a substantial likelihood if more than 66 samples are gathered), it can be provisionally concluded that 95% of oil changes take place in 14.58 ± 2.84 minutes, or, expressed in another manner, in the range between 8.9 minutes and 20.26 minutes. Thus, it can be assumed that only around 5% of oil changes will take over 20 minutes.

Collecting the descriptive statistics of mean and standard deviation is therefore quite informative in terms of creating a marketing campaign. First, the company needs to be able to make a time promise, which will be an important competitive advantage given that consumers want to know how long they can expect to wait for an oil change. Such a time promise cannot be made solely on the basis of the mean number of minutes required for an oil change, because (again, assuming a normal or approximately normal distribution) the mean of 14.58 minutes indicates that only around half of all oil changes take place in 14.58 minutes or less. Therefore, if a promise of 15 minutes were made, this promise would only be kept in around half of all changes, which would severely alienate customers who seek the oil changing service as the result of a time promise. The company would lose even more money if it decided to offer 15-minute service with a money-back guarantee, as, in that case, around half of customers would not be paying for their oil changes.

The calculation of standard deviation allows better use to be made of the mean for purposes of marketing. Because of the characteristics of a normal or approximately normal distribution, it is possible to assume that around 95% of oil changes will take place in less than 20 minutes. Thus, the money lost by having to return the money of 5% of customers is likely to be compensated for by the new customers who are attracted by the 20-minute promise.

Additionally, in the process of generating the histogram for the chosen descriptive statistics, information was found that can help the company further refine its oil change service. Consider the following box plot (see Figure 2 below) of the distribution of oil change minutes:

Previously, the mean of oil change minutes was calculated as being 14.58 minutes, and the standard deviation was 2.84. The data records indicate that one of the oil changes, oil change #54, had a duration of 26 minutes. This duration’s distance from the mean, in terms of standard deviation, can be calculated as follows: Oil change #54 = (26-14.58) / 2.84 = 4.02 standard deviations greater than the mean. Even without the construction of the boxplot, it is simple to deduce that oil change #54 is an outlier, because it took far longer than expected based on the mean and standard deviations for the distribution of the 66 oil changes that were part of the sample. The existence of this outlier is important, because, if we deduce that the conditions that brought about the outlier are hard to replicate, we can recalculate the mean with the outlier and standard excluded. Without the outlier, the mean of the sample actually becomes 14.4, and the standard deviation becomes 2.47.

Because of the lower mean and standard deviation after the removal of the outlier, the company can be more confident in its promise that ‘20 Minutes Or It’s Free!’ 20 minutes is (20-14.4) / 2.47 = 2.27 standard deviations above the mean of 14.4. It can be expected, in a normal distribution, that only around 1.16% of oil changes will last longer than 20 minutes, applying the formula for one-tailed area under the standard normal distribution . Therefore, the company can be highly confident in its promise of 20-minute oil changes. Moreover, this information can be derived solely from a knowledge of the mean and standard deviation of the oil change data, which indicates how useful the mean and standard deviation can be as descriptive statistics.

- Natrella, M. G. (2013). Experimental statistics. New York, NY: Courier Corporation.