statistics
yaser.1
partial_example_for_project_1-1.docx
This is a example of parts of the project to give you an idea of what I am looking for.
Do not use this as a template, but as a reference to a few of the points that may need a little clarification.
This sample includes only parts of the project – parts that I thought might need some clarification on what is expected. The orange font identifies the specific part of the instruction being clarified.
If you have further questions, ask me.
Project 1 sample
Molly Beick
Math 243
Introduction:
I have always thought that big-time movie actors are shorter than the typical man, so I decided to investigate. Working by myself, I gathered a sample list of lead movie actors from featured movies in the television guide, and then looked up their heights on the website http://www.imdb.com/ (internet Movie Data base).
(Objectives)
I decided to look at this topic from two different aspects: what is the average height of movie actors and what proportion of movie actors are 6 feet or taller?
(Populations and Variables)
For the first question, the population is living adult male movie actors who play a prominent role, and my variable is height (measured in inches).
For the second question, the population is again living adult male movie actors who play a prominent role, and my variable is whether or not the actor is taller than 6 feet (72 inches).
The data
(How I collected the data, sample size)
To gather my data, I looked through the television guide in the newspaper. For every movie I found, I wrote down the name of the actor(s) that were listed. I eliminated actors who had passed away or who were children. I then looked up and recorded the heights of the remaining actors on the website http://www.imdb.com/ (internet Movie Data base). I collected only a sample of the population.
Sample size, n = 46 (you need at least 60)
The data I collected is in the chart on the attached page.
(Why did I group the data)
I chose to group the data because it is continuous and continuous data must be grouped to properly represent the information. Also, there are many different values in the data set, which makes grouping the reasonable choice even if the data weren’t continuous.
(Frequency distribution)
Heights frequency
66 – 66.99 1
67 – 67.99 3
68 – 68.99 2
69 – 69.99 4
70 – 70.99 9
71 – 71.99 10
72 – 72.99 4
73 – 73.99 7
74 – 74.99 5
75 – 75.99 1
(Frequency histogram, including values marked)
Descriptive Statistics
Summary Statistics:
Sample size: n = 46
Sample mean: x-bar = 71.06 inches
Sample standard deviation: s = 2.16 inches
Minimum: Min = 66.75 inches
First quartile: Q1 = 70
Median (second quartile): Q2 = 71
Third quartile: Q3 = 73
Maximum: Max = 75.5 inches
Upper Fence: 77.5 (Show your work)
Lower Fence: 65.5
min Q1 Q2 Q3 max
No Outliers
heights in inches
UF = 77.5
LF = 77.5
66.75 70 71 73 75.5
(Complete the table)
|
|
Interval
|
Frequency of my data within the interval (Count to find this) |
percentage of my data within the interval (frequency/n) |
% expected within the interval based on Empirical Rule |
|
|
71.06 + 2.16 = 68.90 in. – 73.32 in. |
34 |
34/46 = 73.9% |
68% |
|
|
71.06 + 2(2.16) = 66.74 in. – 75.48 in. |
45 |
45/46 = 97.8% |
95% |
|
|
71.06 + 3(2.16) = 64.58 in. – 77.64 in. |
46 |
100% |
99.7% |
(Based on table, does Empirical Rule seem to apply? Explain why it should or shouldn’t using information above)
According to my histogram and boxplot, my data appears to come from a fairly symmetric, bell-shaped distribution, so the Empirical Rule should apply. The percentages of my data within the intervals are very close to what is expected by the Empirical Rule. The difference is greatest in the smallest interval, . This difference is by a count of only 2 – 3 more individuals being within the height interval. Looking at the histogram, we can see that the interval just larger than the mean has a higher frequency, which accounts for those extra individuals. Because the sample size is only 46, a small difference (like 2 or 3) in frequency makes for a larger difference in proportion than a large sample would.
Data
|
actor |
height |
in inches |
|
Matt Damon |
5'10" |
70 |
|
Emilio Estevez |
5'7" |
67 |
|
Kevin Spacey |
5'11" |
71 |
|
Tom Cruise |
5'7" |
67 |
|
Tom Hanks |
6'1" |
73 |
|
Will Ferrel |
6'3 1/2" |
75.5 |
|
Ben Stiller |
5'8" |
68 |
|
Matthew McCaunaghy |
6' 1/2" |
72.5 |
|
Greg Kinnear |
5'10" |
70 |
|
Nicolas Cage |
6'1" |
73 |
|
Brad Pitt |
5'11" |
71 |
|
Owen Wilson |
5'11" |
71 |
|
John Travolta |
6'2" |
74 |
|
Richard Gere |
5'10 1/2" |
70.5 |
|
Hugh Grant |
5'11" |
71 |
|
Steve Martin |
6' |
72 |
|
Keanu Reeves |
6'1" |
73 |
|
Johnny Depp |
5'10" |
70 |
|
Orlando Bloom |
5'11" |
71 |
|
Robert DeNiro |
5'10" |
70 |
|
Harrison Ford |
6'1" |
73 |
|
Russell Crow |
5'11 1/2" |
71.5 |
|
Sean Penn |
5'9" |
69 |
|
Eddie Murphy |
5'9.5" |
69.5 |
|
Bill Murray |
6'1" |
73 |
|
Bruce Willis |
6'1" |
73 |
|
Will Smith |
6'2" |
74 |
|
Mel Gibson |
5'10.5" |
70.5 |
|
Robert Downey Jr. |
5'9" |
69 |
|
Colin Farrell |
5'11" |
71 |
|
Robin Williams |
5'8" |
68 |
|
Kurt Russell |
5'10" |
70 |
|
Cary Elwes |
5'11" |
71 |
|
Mike Myers |
5'7" |
67 |
|
Kevin Bacon |
5'11" |
71 |
|
Ethan Hawke |
5 10/5" |
70.5 |
|
Denzel Washington |
6' .5" |
72.5 |
|
Freddie Prinze, Jr |
6'1" |
73 |
|
William H. Macy |
5'9" |
69 |
|
David Duchovny |
6'.5" |
72.5 |
|
Jim Carey |
6'2" |
74 |
|
Wesley Snipes |
5'10" |
70 |
|
Jim Caviezel |
6'2" |
74 |
|
Leonardo DiCaprio |
5'11" |
71 |
|
Ashton Kutcher |
6'2 1/2" |
74.5 |
|
Dustin Hoffman |
5'6 3/4" |
66.75 |
Qualitative Variable: Is the actor 72 inches or taller?
The data
(How I collected the data, sample size)
To gather my data, I looked through the television guide in the newspaper. For every movie I found, I wrote down the name of the actor(s) that were listed. I eliminated actors who had passed away or who were children. I then looked up and recorded the heights of the remaining actors on the website http://www.imdb.com/ (internet Movie Data base). I recorded T (for “Tall”) if he was 72” or over and s (for “short”) if he was not.
I collected only a sample of the population.
Sample size, n = 46 (you need at least 60)
(Raw data)
s s s s T T s T s T s s T s s T T s s s T s s s T T T s s s s s s s s s T T s T T s T s T s
17 are 72” or taller.
Taller than 72” or not frequency relative frequency
T (yes) 17 17/46 = 37%
s (no) 29 29/46 = 63%
The mode is “shorter than 72 inches”
(Explain if the variable is binomial or not)
This is a binomial distribution because
· There are only two possible outcomes
· The population is at least 20 times larger than my sample. 20(46) = 920. There are thousands of adult male actors who have played a significant role in a movie, so the trials are independent and the probability of a success does not change.
· There is a set number of trials – 46 was my sample size
I want to emphasize again, that this should not be used as a template. I intentionally left some of the project out because I want you to use your own words.
Histogram
0
2
4
6
8
10
12
Frequency
Frequency
heights in inches
66 67 68 69 70 71 72 73 74 75 76
heights in inches
mean = 71.06
mean + st.dev. = 73.32
Histogram
0
2
4
6
8
10
12
Frequency
Frequency
heights in inches
66 67 68 69 70 71 72 73 74 75 76
heights in inches
mean = 71.06
mean + st.dev. = 73.32
