Question

All of the following are questions from a statistics video called, what is an average.

1. Does someone always have the median level of some characteristic? This question can provide the opportunity to bring in the concept of interpolation.

2. Are all averages means or medians? You can cite the mode here – though few statisticians use it – or look at the concept of batting average in baseball, which isn’t an average at all but a proportion.

3. What other examples can you think of where most people have more or less than the average? This is true of most things with a non-symmetric distribution (e.g., weight, math scores, marathon times) but it is nice
to continue the theme of the video in terms of risk (e.g., most have below average risk of a automobile accident, death by violence, or even, say, getting a date).

Answer 1

a) If a variable under study has any characteristic that has been quantified and data has been recorded for that characteristic then it is feasible to say that the variable or someone will always have the median level of the characteristic. The median is the central value of the characteristic which is one of the values taken by the recorded data, If the data has 2 or more values then it is suffice to say that the median level of that characteristic will exist. In case of the single value the median level becomes the single value.

b) It is not necessary that all the averages are means and medians. The third form that an average can take is the mode which is the value that has the maximum frequency of occurrence in the dataset. In some cases, one is not bothered about the arithmetic mean of the data or even the central value of the range of dataset. It is the maximum occurrence of a particular value in the dataset that is of interest to us. This value can be at the middle of the range or at an end. For example, the batting score of a baseball player wherein the coach needs to know the maximum number of times the player has scored particular runs. In such cases mode is the nest form of average to be used.

c) There are many times when most people have more or less than the average. Some of the cases are, death in an accident, occurrence of cancer, scoring particular marks in an exam, the rate of a class passing an exam. These examples are innumerable.