1. Compute output for the following quantitative techniques: measures of central tendency and dispersion, correlation, probabilities (basic, binomial, discrete, and normal distribution), sampling and sampling distributions, confidence intervals for means and proportions, one-sample t-tests, two-sample tests (t-tests), one-way and two-way analysis of variance, and simple and multiple linear regression.

2. Interpret the output from the quantitative techniques listed above.

3. Summarize and draw conclusions using the output from the quantitative techniques listed above.

4. Judge the appropriateness of decisions based upon their evaluation of the output from the quantitative techniques listed above.

5. Integrate a Christian worldview into their interpretation and use of quantitative data in organizational decisions.

**Medan, Median, Mode**

**Range**

I am sure the term range is used by you at least once per week. What is the range this vehicle will travel on one fill-up? Ever discuss a wide “range” of topics? Occasionally, a price range is set for an item you wish to purchase. What is the salary range for the job you currently have? Ever have a free-range chicken? Home, home on the range…Range goes from the minimum to the maximum and is discussed daily.

**Standard Deviation**

In many books, they will give you a lot of information about standard deviation without ever explaining what it is. When you hear someone say 40% of all the class earned A’s, or 75% of all cows have difficulty giving milk. You can visualize 40% and 75% by seeing the population in your head. Standard deviation is the same as percentages, only instead of working linear with a whole population; it converts a linear measurement to the area under a bell-shaped curve. Once you become accustomed to using standard deviation, and someone says that the product was almost always within three standard deviations from the mean, you will be able to visualize 68% of the population meeting the standard.

http://www.oxfordmathcenter.com/drupal7/node/290

So then, why use standard deviation? Why not just use percentages? The answer involves many of the formulas that use standard deviation to compute information we wish to know. When we use percentages, it is assumed that the increments increase and decrease steady, one unit at a time. Example 54% to 55% is 1% increase. When using standard deviation you are measuring under a bell shaped curve where the amount of the area about the linear number changes. Look at the curve above, 13.5% and 34% have different areas within the curve. 34% takes up a lot more area. However, look at the linear measurement below, they are the same distance. Each is an additional standard deviation from the mean.

**Z-score**

This is where the z-score comes into play. Looking at the chart above you will see the area under the curve as a percentage and the standard deviation numbers -3 -2 -1 u 1 2 3 as linear measures. The z-score is a chart that converts the percentages to standard deviations and back again. By using the z-tables you can easily say what a percentage is in standard deviation, and you can easily do the reverse. Why is this important? Because many of the formulas used in statistics cannot be run with percentages, they must begin with standard deviations. We convert from percentages to standard deviation (z-score), then we use the formula. When we have the answer, we convert back to the percentages since most people find it easier to understand percentages.

**Coefficient**

Coefficient is one of those words that have always bothered me. It means a number. When I see “coefficient”, I just replace the term for “number”, and everything makes sense.

**Chapter 4**

**Probability**

In fiscal year 2013, Texas revenue for lottery tickets totaled $4,016,791,030. The population of Texas is 26,059,203. Each man, women, and child bought an average of $154.14 in lottery tickets in 2013 or a little less than $3 per week. A household of four was spending $11.85 per week on the lottery.

To win you must have one of the following matches against the number actually drawn:

- Match 6 (Jackpot Win!) Odds = 1:25,827,165
- Match 5 Odds = 1:89,678
- Match 4 Odds = 1:1,526
- Match 3 Odds = 1:75

Overall Odds of a win is 1:71

Is it logical to play the lottery? I will show you how I have already won $36, 232.21 Yes; I have won this, and it was guaranteed. The way I won; I never played. Here is how I did it. Take the $5 my wife and I could have played since the lottery began in my state in 1970. Instead of playing, I put it in the bank. Over the past 44 years, the average interest has been above 5%. By never playing, I have already won over $36,000 and each year I win more. The moral to the story, if you really want to win the lottery, never play.

By the way, there is a difference in the terms “odds” and “probability”. The formula for probability is

(Chances for)

P(x) = ------------------

(Total chances)

The probability of drawing an ace from a single deck of cards is 4/52 = 1/13 or 7.7%

Odds are computed as

(Chances for) : (Chances against)

The odds of drawing an ace in a deck of cards is 4:(52-4) = 4:48 (4 for to 48 against) = 1:12 or 8.3333%

Notice the difference in the second value; probability uses (Total chances), but odds use (Chances against). This is why the probability (if considered as a ratio) and the odds are different. http://mathforum.org/library/drmath/view/56706.html

**Decision Trees**

Decision trees can be enjoyable until there are too many variables. Example: Should I stop grading and watch TV and will I enjoy it if I do? The answer can be yes or no. Assigning a probability to each answer can help me decide. The problem is most assigned numbers are guesses. (There is no chart that says you will enjoy the TV 70% of the time) The percentages are your estimate.

I have a banker friend who uses decision trees to compute the probability of various types of loans defaulting. The problem he had was assigning good probability. What he did was to use historical numbers as his basis. His report turned out to be perfect when the numbers of defaulted loans were calculated the following year. The bank began using his decision tree to determine if the new loans should be approved.

**Bayes’ Theorem**

Thomas Bayes, a Presbyterian minister and mathematician developed “The probability of any event is the ratio between the value at which an expectation depending on the happening of the event ought to be computed, and the value of the thing expected upon its happening”. I read an article claiming this theorem was used when developing the latest software. When you are getting ready to search a topic or file, have you ever been surprised to see it pop up before you select the item? The computer has looked at all of your previous selections and determine the probability of what you will select next. It then selects that item and offers it to you as a time saver.

From *Statistics for Managers*, complete and submit by 11:59 PM central of Day 6:

Submit problems 3.11 (a, b, c), 3.47, 3.49, 4.9, 4.13, 4.23, 4.47 (a, b, c, d, e).

The answers for many of the even-numbered problems are found in the back of the book. It is highly recommended that you work some of these as practice to make sure you understand the concepts before attempting the homework.

Subject | Mathematics |

Due By (Pacific Time) | 09/07/2014 12:00 am |

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