Case 2: Gulf Real Estate Properties. Please provide a Managerial Report that includes: 1. Appropriate descriptive statistics to summarize each of the three variables for the forty Gulf View condominiums 2. Appropriate descriptive statistics to summarize each of the three variables for the eighteen No-Gulf View condominiums 3. Comparison of your summary results from #1 & #2. Discuss any specific statistical results that would help a real estate agent understand the condominium market. 4. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. 5. A 95% confidence interval estimate of the population mean sales price and population mean number of days to sell for Gulf View condominiums. Also, interpret the results. Also, consider the following scenario and include your responses in your Report: 6. Assume the branch manager requested estimates of the mean selling price of Gulf View condominiums with a margin of error of $40,000 and the mean selling price of No-Gulf View condominiums with a margin of effort of $15,000. Using 95% confidence, how large should the sample sizes be?

(2) Descriptive statistics to summarize each of the three variables for the eighteen No-Gulf View condominiums List Price | | Sales Price | | Days to Sell | | | | | | | |

...StandardDeviation (continued)
L.O.: To find the mean and standarddeviation from a frequency table.
The formula for the standarddeviation of a set of data is [pic]
Recap question
A sample of 60 matchboxes gave the following results for the variable x (the number of matches in a box):
[pic].
Calculate the mean and standarddeviation for x.
Introductory example for finding the mean and standarddeviation for a table:
The table shows the number of children living in a sample of households:
|Number of children, x |Frequency, f |xf |x2f |
|0 |14 |0 × 14 = 0 |02 × 14 = 0 |
|1 |12 |1 × 12 = 12 | |
|2 |8 | | |
|3 |6 | |32 × 6 = 54 |
|TOTAL |[pic]...

...StandardDeviation
objective
• Describe standarddeviation and
it’s importance in biostatistics.
Measure of Dispersion
• Indicates how widely the scores
are dispersed around the central
point (or mean.)
-StandarddeviationStandardDeviation.
• The most commonly used method
of dispersion in oral hygiene.
• The larger the standarddeviation,
the wider the distribution curve.
StandardDeviation
• SD, , (sigma)
• Indicates how subjects differ from
the average of the group/ the more
they spread out, the larger the
deviation
• Based upon ALL scores, not just
high/low or middle half
• Analyzes descriptively the spread of
scores around the mean
– 14+ 2.51 = Mean of 14 and SD of
2.51
StandardDeviation
• The spread of scores around the
mean:
• For example, if the mean is 60 and
the standarddeviation 10, the
lowest score might be around 30,
and the highest score might be
around 90.
StandardDeviation &
Variance
Usefulness
• When comparing the amount of dispersion in
two data sets.
• Greater variance = greater dispersion
• Standarddeviation--”average” difference
between the mean of a sample and each data
value in the sample
14+ 2.51 = Mean of 14 and SD of 2.51
Distribution...

...regularly dine at casual restaurants, have eaten at other casual restaurants in the last six months and has a household income of $20,000 or more.
2. What are the demographics of the average Remington’s patron?
b. It should be noted that 59% of patrons are male and only 35% of all respondents can remember seeing an advertisement for Remington’s, Longhorn or Outback in the last 60 days. 75.50% of customers are more familiar with Longhorn or Outback then they are with Remington’s Steakhouse. The average Remington’s patron statistics are listed in Table 1.
Table 1: Demographic Description of the Average Remington’s Patrons
-------------------------------------------------
Variable Mean Central Tendency Variance StandardDeviation
Age 42 2.09 1.45
Gender Male 0.24 0.49
-------------------------------------------------
Number of Children 1 – 2 0.76 0.87
Income $50,001 - $75,000 2.09 1.45
The average Remington’s patron is between 35 and 49 years old, 52% of respondents, and has either has no children, 42% of respondents, or more than 2 children, 31% of respondents. The average income of Remington’s patrons is $62,500 with a relatively evenly spread distribution across the income ranges as shown in Table 2.
Table 2: Reported Income by Remington’s Questionnaire Respondents
-------------------------------------------------
Income Range Percent in Range Percent Above Percent...

...I'll be honest. Standarddeviation is a more difficult concept than the others we've covered. And unless you are writing for a specialized, professional audience, you'll probably never use the words "standarddeviation" in a story. But that doesn't mean you should ignore this concept.
The standarddeviation is kind of the "mean of the mean," and often can help you find the story behind the data. To understand this concept, it can help to learn about what statisticians call normal distribution of data.
A normal distribution of data means that most of the examples in a set of data are close to the "average," while relatively few examples tend to one extreme or the other.
Let's say you are writing a story about nutrition. You need to look at people's typical daily calorie consumption. Like most data, the numbers for people's typical consumption probably will turn out to be normally distributed. That is, for most people, their consumption will be close to the mean, while fewer people eat a lot more or a lot less than the mean.
When you think about it, that's just common sense. Not that many people are getting by on a single serving of kelp and rice. Or on eight meals of steak and milkshakes. Most people lie somewhere in between.
If you looked at normally distributed data on a graph, it would look something like this:
The x-axis (the horizontal one) is the value in question......

...the information provided by the StandardDeviation.
2. The ability to use the StandardDeviation to calculate the percentage of occurrence of a variable either above or below a particular value.
3. The ability to describe a normal distribution as evidenced by a bell shaped curve as well as the ability to prepare a distribution chart from a set of data (module 3 Case).
Part 1
(1) To get the best deal on a CD player, Tom called eight appliance stores and asked the cost of a specific model. The prices he was quoted are listed below:
$ 298 $ 125 $ 511 $ 157 $ 231 $ 230 $ 304 $ 372 Find the Standarddeviation
$ 298 + $ 125+ $ 511+ $ 157+ $ 231+ $ 230+ $ 304+ $ 372= 2228/8 = 278.5(subtract from #s)
19,-153, 232, -121, -47, -48, 25, 93 (square numbers)
380, 2356, 54056, 14762, 2256, 2352, 650, 8742 = 106(added)
(Divide by 7) 15251 (take square root) StandardDeviation = approximately 123.
(2) When investigating times required for drive-through service, the following results (in seconds) were obtained. Find the range, variance, and standarddeviation for each of the two samples, and then compare the two sets of results.
Wendy's 120 123 153 128 124 118 154 110
MacDonald's 115 126 147 156 118 110 145 137
(2) Set 1:
Range : maximum - minimum = 154-110= 44...

...MEASURES
MULTIPLE CHOICE QUESTIONS
In the following multiple choice questions, circle the correct answer.
1. Which of the following provides a measure of central location for the data?
a. standarddeviation
b. mean
c. variance
d. range
Answer: b
2. A numerical value used as a summary measure for a sample, such as sample mean, is known as a
a. population parameter
b. sample parameter
c. sample statistic
d. population mean
Answer: c
3. Since the population size is always larger than the sample size, then the sample statistic
a. can never be larger than the population parameter
b. can never be equal to the population parameter
c. can be smaller, larger, or equal to the population parameter
d. can never be smaller than the population parameter
Answer: c
4. ( is an example of a
a. population parameter
b. sample statistic
c. population variance
d. mode
Answer: a
5. The hourly wages of a sample of 130 system analysts are given below.
mean = 60 range = 20
mode = 73 variance = 324
median = 74
The coefficient of variation equals
a. 0.30%
b. 30%
c. 5.4%
d. 54%
Answer: b
6. The variance of a sample of 169 observations equals 576. The standarddeviation of the sample equals
a. 13
b. 24
c. 576
d. 28,461
Answer: b
7. The median of a sample will always equal the
a. mode
b. mean
c. 50th...

...the new point on the standarddeviation?
The new point has made the standarddeviation to go up to over 2.07
b) Follow the instructions to create the next two graphs then answer the following question: What did you do differently to create the data set with the larger standarddeviation.
What I did differently was to have two outliners on both ends of the outline so I can create the largerstandarddeviation and also to keep the mean at five.
2. Go back to the applet and put points matching each of the following data set into the first graph of the applet and clear the other two graphs. Set the lower limit to 0 and the upper limit to 100.
50, 50, 50, 50, 50
Notice that the standarddeviation is 0. Explain why the standarddeviation for this one is zero. Don’t show just the calculation. Explain in words why the standarddeviation is zero when all of the points are the same.
There’s not a deviation from this sample because all the data points are equal to each other.
3. Go back to the applet one last time and set all 3 of the lower limits to 0 and upper limits to 100. Then put each of the following three data sets into one of the graphs.
Data set 1: 0, 25, 50, 75, 100
Data set 2: 30, 40, 50, 60,...

...Standarddeviation can be difficult to interpret as a single number on its own. Basically, a small standarddeviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standarddeviation means that the values in the data set are farther away from the mean, on average.
The standarddeviation measures how concentrated the data are around the mean; the more concentrated, the smaller the standarddeviation.
A small standarddeviation can be a goal in certain situations where the results are restricted, for example, in product manufacturing and quality control. A particular type of car part that has to be 2 centimeters in diameter to fit properly had better not have a very big standarddeviation during the manufacturing process. A big standarddeviation in this case would mean that lots of parts end up in the trash because they don’t fit right; either that or the cars will have problems down the road.
But in situations where you just observe and record data, a large standarddeviation isn’t necessarily a bad thing; it just reflects a large amount of variation in the group that is being studied. For example, if you look at salaries for everyone in a certain company,...