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Math - Statistics Methodology











































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.
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.
Sample at least fifteen people and record their data in a simple table or chart; study the examples from Section 12-3.
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?
Explain in moderate detail the method you used to gather your data. In statistics this venture is called the “Methodology.”
Make sure you break your sample into classes or groups, such as males/females, or ages, or time of day, etc.
Calculate the mean, median, and mode for your data as a whole.
Now calculate the mean, median, and mode of each of your classes or groups.
Indicate which measure of central tendency best describes your data and why. Then compare your results 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 (i.e., between men and women).

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Apr 15, 2011
Math - Statistics Methodology
by: Staff

-------------------------------------------------------------
Part III

Calculate the mean, median, and mode of each of your classes or groups.

Men: sleep hours reported

5
5.5
5.75
6.5
6.5
6.75
7
7.25
7.5
8


Mean (average) for men:

mean (average) = (5+5.5+5.75+6.5+6.5+6.75+7+7.25+7.5+8)/10
= 6.6 hours

Median for men = 6.63 hours

5
5.5
5.75
6.5
6.5
median = (6.5+6.75)/2 = 6.63
6.75
7
7.25
7.5
8


Mode for men: 6.5 hours

Plot a histogram which shows the frequency of occurrences versus hours reported

5.00 x
5.50 x
5.75 x
6.50 xx************* mode (2 occurrences)
6.75 x
7.00 x
7.25 x
7.50 x
8.00 x



Female: sleep hours reported

6.5
6.75
7.5
7.5
7.75
8
8.25
8.5
8.5
8.75


Mean (average) for females:

mean (average) = (6.5+6.75+7.5+7.5+7.75+8+8.25+8.5+8.5+8.75)/10
= 7.8 hours


Median for females = 7.88 hours

6.5
6.75
7.5
7.5
7.75
median = (7.75+8)/2 = 7.88
8
8.25
8.5
8.5
8.75


Mode for females: bimodal: There are two modes: 7.5 hours and 8.5 hours


Plot a histogram which shows the frequency of occurrences versus hours reported

6.50 x
6.75 x
7.50 xx ************* mode (2 occurrences)
7.75 x
8.00 x
8.25 x
8.50 xx ************* mode (2 occurrences)
8.75 x


Which measure of central tendency best describes your data and why.

The mean and median are relatively close for all three groups (total, men, and women). Either the mean or the median appear to be good indicators of central tendency.

The modes which do occur are small.



Comparative Analysis

The majority of people do get less than 8 hours sleep during the work week. 70 % of those surveyed (14 out of 20 people) reported getting less than 8 hours sleep per night.

Males sleep less than females. On average, males get 1.2 hours less sleep than females each night.

Overall, there appears to be two groups of people who concentrate their sleep habits around 6.5 and 7.5 hours of sleep per night.



Thanks for writing.


Staff
www.solving-math-problems.com

Apr 15, 2011
Math - Statistics Methodology
by: Staff


-------------------------------------------------------------
Part II

Sample at least fifteen people and record their data in a simple table or chart


20 people surveyed

male - no. 1 - less than 6 hours (5 hours)
female - no. 2 - 7 to 7.9 hours (7.5 hours)
female - no. 3 - 8 hours or more (8.5 hours)
female - no. 4 - 6 to 6.9 hours (6.75 hours)
male - no. 5 - 6 to 6.9 hours (6.5 hours)
female - no. 6 - 7 to 7.9 hours (7.5 hours)
male - no. 7 - less than 6 hours (5.5 hours)
male - no. 8 - 7 to 7.9 hours (7.25 hours)
female - no. 9 - 8 hours or more (8.75 hours)
male - no. 10 - 6 to 6.9 hours (6.75 hours)
female - no. 11 - 8 hours or more (8.25 hours)
male - no. 12 - 7 to 7.9 hours (7 hours)
female - no. 2 - 8 hours or more (8 hours)
male - no. 14 - 6 to 6.9 hours (6.5 hours)
male - no. 15 - 7 to 7.9 hours (7.5 hours)
male - no. 16 - 8 hours or more (8 hours)
female - no. 17 - 8 hours or more (8.5 hours)
male - no. 18 - less than 6 hours (5.75 hours)
female - no. 19 - 7 to 7.9 hours (7.75 hours)
female - no. 20 - 6 to 6.9 hours (6.5 hours)

all people surveyed:

3 people - less than 6 hours sleep
5 people - 6 to 6.9 hours sleep
6 people - 7 to 7.9 hours sleep
6 people - 8 hours or more sleep

Subgroup: males surveyed:

3 people - less than 6 hours sleep
3 people - 6 to 6.9 hours sleep
3 people - 7 to 7.9 hours sleep
1 person - 8 hours or more sleep

Subgroup: females surveyed:

0 people - less than 6 hours sleep
2 people - 6 to 6.9 hours sleep
3 people - 7 to 7.9 hours sleep
5 people - 8 hours or more sleep

Which of the four sampling techniques best describes your design?

Data was gathered by phone.


Calculate the mean, median, and mode for your data as a whole.



mean (average) = (5+7.5+8.5+6.75+6.5+7.5+5.5+7.25+8.75+6.75+8.25+7+8+6.5+7.5+8+8.5+5.75+7.75+6.5)/20
= 7.2 hours

Median = 7.38 hours

To find the median, sort the number of hours reported from lowest to highest, and then find the middle number. Since there are an even number of data points for this survey, average the two middle numbers:

5
5.5
5.75
6.5
6.5
6.5
6.75
6.75
7
7.25
median = (7.25+7.5)/2 = 7.38
7.5
7.5
7.5
7.75
8
8
8.25
8.5
8.5
8.75


Mode: This distribution is bimodal: There are two modes: 6.5 hours and 7.5 hours


Plot a histogram which shows the frequency of occurrences versus hours reported

5.00 x
5.50 x
5.75 x
6.50 xxx ************* mode (3 occurrences)
6.75 xx
7.00 x
7.25 x
7.50 xxx ************* mode (3 occurrences)
7.75 x
8.00 xx
8.25 x
8.50 xx
8.75 x

-------------------------------------------------------------

Apr 15, 2011
Math - Statistics Methodology
by: Staff

Part I
The question:
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.
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.
Sample at least fifteen people and record their data in a simple table or chart; study the examples from Section 12-3.
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?
Explain in moderate detail the method you used to gather your data. In statistics this venture is called the “Methodology.”
Make sure you break your sample into classes or groups, such as males/females, or ages, or time of day, etc.
Calculate the mean, median, and mode for your data as a whole.
Now calculate the mean, median, and mode of each of your classes or groups.
Indicate which measure of central tendency best describes your data and why. Then compare your results 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 (i.e., between men and women).


The answer:

Select a topic


How many hours so people sleep each day?

--------------------------------------------------------

Note: The figures used to answer your question are fictitious estimates, and are presented for demonstration purposes only. They are based on the 2002 report issued by the National Sleep Foundation. That report can be downloaded in pdf format here:

http://www.sleepfoundation.org/sites/default/files/2002SleepInAmericaPoll.pdf

--------------------------------------------------------


Write a hypothesis of what you expect your research to reveal.

On weekdays, most people sleep less than 8 hours per day.


Methodology: Explain in moderate detail the method you used to gather your data.

Data was gathered by phone.

Only one question was asked: On average, how many hours per night do you sleep from Sunday night through Thursday night?

-------------------------------------------------------------

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