Choose and write down 12 distinct (different) positive integers (no modes), each less than 100, in a way that the data set would have a range of 92, a mean of 60, and a median of 56

(a)In order not to treat the data as an abstract set, state what the data might represent with an applicable unit.

The values represents the age of people attending the annual training meeting.

(b)Show the data set and the work to demonstrate that the data set does have the statistical characteristics mentioned. Consider the data set as a sample.

(c)Estimate the standard deviation using the "range rule of thumb," which is based on the fact that four standard deviations practically cover the span of the data (about 95% for normal distributions), when rank ordered.To save time, do not calculate the actual standard deviation value using its formula for this part.The standard deviation found would have the same unit as in Part (a) above; the unit should accompany the value when reported.

What would be an estimate for the variance?

(d)Use technology (for example, the "Variance and Standard Deviation Applet," provided under

Content > Course Resources > Free Web Applets in LEO) to find the actual values (in two decimal places) for the variance (with its unit) and the standard deviation (with its unit) of the data set, considered as a sample.

If you mistakenly treated the data set as a population, the actual values for the variance and the standard deviation would be relatively lower.Explain Why?

(e)Provide the five-number summary.

(f)Determine the Interquartile Range (IQR).

(g)Provide a box-and-whisker plot for the data set. Determine outliers, if any? Briefly explain how outliers can be detected.

(h)Using the "actual value" for the standard deviation (STD) from Part (d) above, determine what percentage of the data points would fall within one STD of the mean, i.e., within the interval (mean - STD, mean + STD).Compare the answer with the Empirical Rule percentage.Briefly the inconsistency, if any.