Practical Aplications Of Satistics

Practical Application of Statistics

Mean, Median, and Mode

Assume that five bids are received for an engineering project, with total costs of $22,000; $35,000; $37,000; $40,000; and $65,000. The mean, or arithmetic average, of the bids is $39,800. The median, which is defined as the middle value when the numbers are arranged in ascending or descending order, is $37,000. If an even number of values are given, the median is typically "the arithmetic mean of the two middle observations" and "may not be one of the given values" (Lind et. al., 2002, p. 72). The mode is defined as "the value of observation that appears most frequently" (p. 74). Since all of the bids are different, there is either no mode or every value is the mode (p. 75).

Central Tendency

Central tendency is "a single value that summarizes a set of dataÐ'...(and) locates the center of values" (p. 65). For any group of values, the mean, median, or mode could be used as the measure of central tendency. In the example above, either the mean or median could be used as the measure of central tendency since their values are similar. However, if only the bids of $35,000; $37,000, and $65,000 were received, the median value of $37,000 might be a better indicator of central tendency. It is not unusual for one bid to be much different, either higher or lower, than the other bids. Typically, when bids are evaluated, the bids that differ widely from the others would be eliminated from consideration. For the three bids listed, the two bids that are close in value can be assumed to be a better indicator of the cost of the project, while the highest bid could be assumed to be a result of inflating the true cost. In the first example of five bids, the low and high bid might be eliminated, with the assumption that the low bid resulted from an unrealistic projection of the costs.

Sampling

Proper sampling requires that the sample "must be Ð''representative' of the population. If it is Ð''representative' of the population, it will not overemphasize or underemphasize any characteristic of the population (it will not be biased). Second, a good sample must provide the level of confidence and the level of error (in the result) that is acceptable to the researcher" (Lenert, Lecture #2, para. 3). Additionally, "in order for a sample to be Ð''representative,' it must be selected in a way that gives every member of the population a chance to participate in the sample" (para. 4).

We extract samples from the exit piping of a tank to monitor changes to the product caused by process changes upstream of the tank. An engineering principal states that the total volume of a tank must be replaced three times to be 95% confident that the outlet stream is representative of an upstream change. For the tank that we