Week Five Discussion

This Discussion will give you the opportunity to calculate or identify the three measures of central tendency. You will be asked to select an appropriate real life situation in which one measure would be more appropriate than the other two measures of center. 1. Select a topic of interest to you and record the topic in your posting, for example: “What is the average number of hours people watch TV every week?” Make sure the question you ask will be answered with a number, rather than answers with words. What is the average number of hours people read every week?
2. Write a hypothesis of what you expect your research to reveal. Example: Adults 21 years and over watch an average of 2.5 hours of TV per day. On average, people read about 15 hours per week.
3. Sample at least fifteen people and record their data in a simple table or chart; study the examples from Section 123. PERSON AGE GENDER HOURS READ PER WEEK
1 17 F 8
2 16 F 10
3 14 F 5
4 37 M 4
5 38 F 20
6 33 F 5
7 22 F 30
8 52 F 30
9 40 F 18
10 21 M 3
11 16 F 14
12 13 M 5
13 36 F 25
14 27 F 20
15 43 F 25
4. 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? Out of the four sampling techniques, the one that I believe best describes my design would be the random sample method.
5. Explain in moderate detail the method you used to gather your data. In statistics this venture is called the “Methodology.” The method I used to gather my data is from my Facebook friends. I do not venture out much so I was going to have a better chance gaining information that way. So, I posted that I needed information on how many hours a week that they read and their age. 6. Make sure you break your...
...Answer the following problems showing your work and explaining (or analyzing) your results.
1. Describe the measures of centraltendency. Under what condition(s) should each one be used?
Mean Works good when it comes to test scores
Median should be used when describing something like average income.
Mode= is good is you want to see what is you best seeing product in a store situation.
2. Last year, 12 employees from a computer company retired. Their ages at retirement are listed below.First, create a stem plot for the data. Next, find the mean retirement age. Round to the nearest year.
55 77 64 77 69 63 62 64 85 64 56 59
8
5
7
77
6
234449
5
569
Mean = 66
3. A retail store manager kept track of the number of car magazines sold each week over a 10week period. The results are shown below.
27 30 21 62 28 18 23 22 26 28
a. Find the mean, median, and mode of newspapers sold over the 10week period.
285
Mean= 28.5
Median=26.5
Mode=28
b. Which measure(s) of centraltendency best represent the data?
Mean
c. Name any outliers. 62
d. Joe wants to pass his statistics class with at least a 75%. His prior four test scores are 74%, 68%, 84% and 79%. What is the minimum score he needs on the final exam to pass the class with a 75% average?...
...
Subject: Math – Measures of CentralTendency
Grade: 6th
GLE Standard: Mathematics  Data and Probability. 2. Select and use appropriate statistical methods to analyze data. A. Describe and analyze data  find the range and measures of center, including median, mode, and mean.
Materials:
 Bag of mixed candy, or something comparable the students can sort and count
 Whiteboard/blackboard
 Computer and display ability
 Legal sized paper or construction paper
Objectives/Learning Targets: By analyzing a set of data, students will be able to calculate mean, median, mode, and range.
Introduction:
 After greeting the class show a short video, on mean, median, mode, and range, called “Measures of CentralTendency Rap” http://www.youtube.com/watch?v=1jVZi0cNHls
 Give the students a Handout highlighting the key concepts of mean, median, mode, and range, as well as some example problems and the steps to work them
 Next, show the class a large bag of assorted candy, for example a 105 count bag of assorted Easter candy, and ask the class to guess the amount of each candy type
 Finally, group students and distribute the candy (so the students can be ready to sort and count the candy)
Lesson Procedure:
Modeling/Teaching: With the help of the students, separate...
...Introduction to Statistics (Measures of CentralTendency)
CentralTendency: In a representative sample, the value of a series of data have a tendency to cluster around a certain point usually at the center of the series is usually called centraltendency and its numerical measures are called the measures of centraltendency or measures of location.
Different Measures of CentralTendency: The following are the important measures of centraltendency which are generally used in business:
Arithmeticmean
Geometric mean
Harmonic Mean
Median
Mode
Arithmeticmean: Arithmeticmean is defined as the sum of all observations divided by the total number of observations.
Calculation of ArithmeticMeanUngrouped Data: For ungrouped data, arithmeticmean may be computed by applying any of the following methods:
Direct method
Shortcut method
Direct method: The arithmeticmean, often simply referred to as mean, is the total of the values of a set of observations divided by their total number of observations. Thus, if represent the values of items or observations, the...
...Assignment on CentralTendency and Dispersion
1. A manufacturer of hand shovels is deciding what length handles to use. Studies of user preference reveal that the average, the median, mean and mode of preferred length are all different. What are the implications of using each of these values? Which value would you decide?
2. A given machine is assumed to depreciate 40 percent in value in the first year, 25 percent in value in the 2nd year and 10 percent in value in the next three years; each percentage is being calculated on the diminishing value. What is the average percentage depreciation, reckoned on the diminishing value for the five years?
3. The mean age of a group of 100 persons was found to be 32.02.Later, it was discovered that age 57 was misread as 27. Find the corrected arithmeticmean.
4. Out of the total population of certain town in South Africa 60% belonged to the Black Race and the rest belonged to the white race. It was estimated that their mean incomes were 2000 and 5000 pounds respectively. Find the average income of the entire town?
5. The following data represents travel expenses (other than transport) for trips made during November by a salesman of a firm.
Trip Days Expense Expense per day
1 .5 13.50 27.00
2 2 12.00 6.00
3...
...Prices are in thousands of dollars.
Those analyses are below:
Descriptive Statistics for Gulf View
Gulf View List Price  Gulf View Sales Price  Gulf View Days to Sell 
Mean  474.0075  Mean  454.2225  Mean  106 
Median  437  Median  417.5  Median  96 
Maximum  975  Maximum  975  Maximum  282 
Minimum  169.9  Minimum  165  Minimum  28 
Standard Deviation  197.29003  Standard Deviation  192.5177534  Standard Deviation  58.2168207 
Based on the chart, the mean was calculated by adding up the sum of the list and divide 40, which the number of the total listed prices. The mean is 474,007.5, which mean the average of the listed price. Secondly, the median was calculated by listing the number in numerical order from lowest to highest and located the number in the middle 437,000. The median represents the middle number of the listed price. After calculating the median I located the minimum and maximum based the lowest and highest data, which are 169,900 and 975,000. These represent the range of the listed price. Lastly, I used the formula to get the standard deviation of 197,290.03, which measures the variability.
To calculate the mean I added up the sum sale price and divide 40, which the number of the total sale prices. The mean is 454,222.5, which mean the average of the listed price. The median...
...Measures Of CentralTendency: Mean Medium Mode
Mode instead of mean… Categorical variables, words not numbers
Measures of Dispersion: Standard Deviation, Range, and Variables
Range = Largest number minus smallest number
SD = Average Distance from the Mean (Most frequently used)
Variance:
Fat & Skinny Distributions: Skewness – measure of the lack of symmetry, or the lopsidedness of a distribution.
One “tail” of the distribution is longer than another.
Kurtosis: has to do with how flat or peaked a distribution appears/
Platykurtic: flat
Leptokurtic: peake
Hypotheses
Null Hypothesis: There is NO RELATIONSHIP between our IV and DV
NonDirectional Hypothesis:
Directional Hypothesis: We believe we know the direction
What makes a good hypothesis?
Testable
Can’t be in a question
Tell a relationship between
Stated in a declarative form
Brief and to the point
Reflects theory or past literature
Tells a relationship between variables
The Normal Curve
The Bell Shaped Curve
Mean=Median=Mode
Symmetrical
Asymmetric Curve
Statistical Inference
The Central Limits Theorem: When samples are large (above 30) the sampling distribution will take the shape of a normal distribution regardless of the shape of the population
Ultimate Goal
Accepting or Rejecting the NULL hypothesis
Accept or Reject?
We accept a...
...information to optimally plan their ski classes. Define the following in terms of the study. Give examples where appropriate.
Population Children who take ski or snowboard lessons
Sample A group of these children
Parameter The mean of population
Statistic The mean of the sample
Variable The age of one child who takes the first ski or snowboard lesson
Data The values of the variable, such as age 7 etc..
EXERCISE 6
A cardiologist is interested in the average recovery period for her patients who have had heart attacks. Define the following in terms of the study. Give examples where appropriate.
Population Patients who have had heart attacks.
Sample A group of the patients
Parameter The mean of the population
Statistic The mean of the sample
Variable The recovery period for one patient who have had heart attack
Data The values of the variable, such as 3 etc..
EXERCISE 7
Insurance companies are interested in the average health costs each year for their clients, so that they can determine the costs of health insurance. Define the following in terms of the study. Give examples where appropriate.
Population The clients of the insurance companies
Sample A group of the clients
Parameter The mean health costs of the clients
Statistic The mean health costs of the sample
Variable the health costs of one client
Data The values of the variable, such as 9 etc.
...
...
Investment Category Arithmetic Geometric Standard Deviation
MeanMean Of Return
Common Stocks 10.28% 8.81% 16.90%
Treasury Bills 3.54% 3.49% 3.20%
Longterm govern. Bonds 5.10% 4.91% 6.40%
Longterm corpor. Bonds 5.95% 5.65% 9.60%
Real Estate 9.49% 9.44% 4.50%
a). Explain why the geometric and arithmeticmeans are not equal and whether one or the other
may be more useful for investment decision making.
Arithmeticmean is the sum of a series of numbers divided by the count of that series of numbers.
Am = (a1+a2+a3+…+an)/n
Geometric mean is the nroot of a series of numbers by multiplying them.
Gm = n√(a1*a2*a3*…*an)
From the equations above it is obvious that the arithmeticmean is always greater than the geometric mean,or it could be equal.
The Geometric mean could be used for summarizing the effect on investment returns.
The Arithmeticmean could be used for calculating expected or average return over one period of time.
Therefore, if the intent is to accurately summarize and report past returns the geometric mean must be used.
b). For the time period indicated, rank...
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