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Discussing the Distribution of a Data Population

There are several measures of central tendency. By far the most frequently utilized of these measures is the mean of a population. Remember that the source of the data that you want to analyze always comes from what is called a population. If you are interested in the average high temperature in your area for the month of July, then your population would be the 31 daily high temperatures in July, and the mean would be the total of these temperatures divided by 31.

Now, suppose you calculate a mean of a population and you want to know how representative that mean is of a random data point in that population. In other words, is the data bunched tightly around the mean, or is it more loosely distributed over the possible range of values? An example would be high temperatures in July versus high temperatures in April or October. In general, the highs in April and October will vary more widely from the means in those months than the highs in July.

In summary, it takes not only the mean to adequately describe a population, but there must be some way to measure the dispersion, or distribution, of the data around the mean.

What is the definition of what is called the distribution of a data population?

Also, find the statistic that measures the width of dispersion ("looseness" or "tightness") of the population data about its mean. Give an example of the type of situation where this statistic might be critical to making good decisions about the population under study.

Solution Preview

Overview of Mean, Median and Mode

Mean:

The mean is the arithmetic average, or simply the average, of a set of scores. You are probably more familiar with it than any other measure of central tendency. You encounter the mean in everyday life whenever you calculate your exam average, batting average, gas mileage average, or a host of other averages.

Median:

The median is the middle score in a distribution of scores that have been ranked in numerical order. If the median is located between two scores, it is assigned the value of the midpoint between them (for example, the median of 23, 34, 55, and 68 would equal 44.5). The median is the best measure of central tendency for skewed distributions, because it is unaffected by extreme scores. Note that in the example below the median is the same in both sets of exam scores, even though the second set contains an extreme score. The mean is quite different, due to the one extreme score on Exam B.

Exam A: 23, 25, 63, 64, 67

Exam B: 23, 25, 63, 64, 98

3. The median home price in your area has increased in the last 10 years, how does this differ from the mean home price in your area?

As described above the median is middle score in a distribution of scores that have been ranked in numerical order. If the median is located between two scores, it is assigned the value of the midpoint between them. The increase in median home price means that there is increase in middle price of home of our area.

Mean home price is simply the average, of a set of scores. So it can be affected by any extreme value. Therefore mean is not a good representative of the data in case of skewed distribution.

In statistics, the mode is the value that has the largest number of observations, namely the most frequent value or values. The mode is not necessarily unique, unlike the arithmetic mean.

It is especially useful when the values or observations are not ...

Solution Summary

This solution is comprised of a very detailed response of over 1200 words that discusses the concept of the distribution of a data population. Many statistical concepts are discussed and examples are provided. One reference is also included at the end of the discussion.

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