Homework answers / question archive / Each of the three measures of central tendency?the mean, the median, and the mode?are more appropriate for certain populations than others

Each of the three measures of central tendency?the mean, the median, and the mode?are more appropriate for certain populations than others

Statistics

Share With

---

Each of the three measures of central tendency?the mean, the median, and the mode?are more appropriate for certain populations than others. For each type of measure, give two additional examples of populations where it would be the most appropriate indication of central tendency.

2. Find the mean, median, and mode of the following data set:
5 15 9 22 67 42 2 72 81 53 6 70 41 9 42 23

3. Sometimes, we can take a weighted approach to calculating the mean. Take our example of high temperatures in July.

Suppose it was 98°F on 7 days, 96°F on 14 days, 88°F on 1 day, 100°F on 6 days and 102°F on 3 days.
Rather than adding up 31 numbers, we can find the mean by doing the following:
Mean = ( 1 x 88 + 14 x 96 + 7 x 98 + 6 x 100 + 3 x 102) / 31
...where 1, 14, 7, 6, and 3 are the weights or frequency of a particular temperature's occurrence.
Then we divide by the total of number of occurrences.

Suppose we are tracking the number of home runs hit by the Boston Red Sox during the month of August:

Number of Games HRs Hit each Day
2 3
5 2
6 1
7 0

Using the weighted approach, calculate the average number of home runs per game hit by the Sox.

4. When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over.

A. Why will some numbers come up more frequently than others?

B. Each die has six sides numbered from 1 to 6. How many possible ways can a number be rolled? In other words, we can roll (2,3) or (3,2) or (6,1) and so on. What are the total (x,y) outcomes that can occur?

C. How might you then estimate the percentage of the time a particular number will come up if the dice are rolled over and over?

D. Once these percentages have been calculated, how might the mean value of the all the numbers thrown be determined?

E. If you have completed part 2 already, you have an idea of what a population distribution is.

There is a very famous distribution that describes the frequency of the number of times a number comes up in a series of dice rolls.

Use the Internet to see if you can find its name.

Part 2

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.

Problem -

1.Use the Internet to research the definition of what is called the distribution of a data population.

2.Also, find the statistic that measures the width of dispersion ("looseness" or "tightness") of the population data about its mean.

3.Give an example of the type of situation where this statistic might be critical to making good decisions about the population under study.