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# Measuring Central Tendency

This Discussion will give you the opportunity to calculate or identify the three measures of central tendency. Select an appropriate real life situation where one measure would be more appropriate than the other two measures of center.

a. Select a common topic or hypothesis and record the topic in your posting, for example: "What is the average number of hours you watch TV every week?" You may use one of your Week Four hypotheses.
b. Sample at least 15 people and record their data in a simple table or chart;
c. You can gather your data at work, on the phone, or via some other method. This is your "Sampling Design." Which of the four sampling techniques best describes your design?
d. Explain in moderate detail the method you used to gather your data. In statistics this venture is called the "Methodology."
e. Make sure you break your sample into classes or groups, such as: males/females or ages or time of day, etc.
f. Calculate the mean, median, and mode for your data as a whole.
g. Now calculate the mean, median, and mode of each of your classes or groups.
h. Indicate which measure of central tendency BEST describes your data and WHY.
i. Now compare your results in part h for each class or group, and point out any interesting results or unusual outcomes between the classes or groups. This is called a "comparative analysis" - using our results to explain interesting outcomes or differences (for example, between men and women).

#### Solution Preview

This Discussion will give you the opportunity to calculate or identify the three measures of central tendency. Select an appropriate real life situation where one measure would be more appropriate than the other two measures of center.

a. Select a common topic or hypothesis and record the topic in your posting, for example: "What is the average number of hours you watch TV every week?" You may use one of your Week Four hypotheses.

My topic will be "How tall are you in inches?"

b. Sample at least 15 people and record their data in a simple table or chart;

This data is completely made up. When you do this assignment, you should sample people yourself and get real data.

Person Height (inches)
1 64
2 60
3 72
4 74
5 69
6 68
7 61
8 65
9 70
10 70
11 71
12 63
13 65
14 70
15 68
16 65
17 63
18 63
19 66
20 67

c. You can gather your data at work, on the phone, or via some other method. This is your "Sampling Design." Which of the four sampling techniques best describes your design?

There are several different ways to gather data. They each have their own advantages and disadvantages. The wikipedia entry on sampling methods has a good (and accurate) description of sampling techniques:

Sampling method
Within any of the types of frame identified above, a variety of sampling methods can be employed, individually or in combination. sampling is divided in two categories 1. Probability Sampling 2. Nonprobability Sampling
Probability sampling includes: Simple Random Method, Systematic Sampling, Stratified Sampling and Cluster or Multistage Sampling.&#8232;Nonprobability Sampling includes: Accidental Sampling, Quota Sampling and Purposive Sampling.

Simple random sampling
In a simple random sample of a given size, all such subsets of the frame are given an equal probability. Each element of the frame thus has an equal probability of selection: the frame is not subdivided or partitioned. It is possible that the sample will not be completely random.
Systematic sampling
Selecting (say) every 10th name from the telephone directory is called an every 10th sample, which is an example of systematic sampling. It is a type of probability sampling unless the directory itself is not randomized. It is easy to implement and the stratification induced can make it efficient, but it is especially vulnerable to periodicities in the list. If periodicity is present and the period is a multiple of 10, then bias will result. It is important that the first name chosen is not simply the first in the list, but is chosen to be (say) the 7th, where 7 is a random integer in the range 1,...,10-1. Every 10th sampling is especially useful for efficient ...

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