Skills 8, 9, 10

Skills Goals: Create Dot plots, Stemplots, and Histograms, using small sets of observations.

Dot plots- A statistical chart consisting of a group of data points plotted on a scale. Dot plots are used for continuous, quantitative, and univariate data. Dot plots are one of the simplest statistical plots, and are suitable for small to moderate sized data sets. They are useful for highlighting clusters and gaps, as well as outliers.

Example of a Dot plot:

Practice Problems:

1) The ages of the Oscar winners for best actor and best actress (at the time they won the award) from 1996 to 2004 are as follows: 45, 39, 59, 33, 45, 25, 42, 24, 35, 32, 46, 32, 28, 34, 42, 27, 36, and 30. Create a dot plot of these data and discuss what the display implies about the data.

2) Twenty high school students were randomly selected from a very large high school. They were asked to keep a record for a week of the number of hours they slept each night. These seven values were averaged to obtain an average night of sleep for each. The results are as follows: {9, 8, 8, 7.5, 6, 6, 4, 5.5, 7, 8, 5, 7.5, 6.5, 10, 8.5, 6.5, 5, 5.5, 7, 7.5}. Create a dot plot of these data and discuss what the display implies about the data.

Stemplots- Also known as a Stem and Leaf plot, a stem plot is a device for presenting quantitative data in a graphical format. A basic stemplot contains two columns separated by a vertical line. The left column contains the stems and the right column contains the leaves. Stemplots are useful for displaying the relative density and shape of the data, giving the reader a quick overview of distribution. They are useful for medium sets of data between 10-100.

An example of a Stem plot:

UMMMMMMM....I haven't figured out how to use the Diigo thing yet, so heres an interactive link to help you learn how to do stem and leaf plots.

http://www.wisc-online.com/Objects/ViewObject.aspx?ID=tmh1101

Practice Problems:

1) Ms. Reed's AP Physics class took a test last Thursday. Make a stem and leaf plot of the test scores given: {56, 65, 98, 82, 64, 71, 78, 77, 86, 95, 91, 59, 69, 70, 80, 92, 76, 82, 85, 91, 92, 99, 73}

2) In the month of April, the Weather Channel took the average temperature of each day for the entire month: {77, 80, 82, 68, 65, 59, 61, 57, 50, 62, 61, 70, 69, 64, 67, 70, 62, 65, 65, 73, 76, 87, 80, 82, 83, 79, 79, 71, 80, 77}. Using this data, construct a stem and leaf plot to help the Weather Channel.

Histograms- Histograms are used to plot density of data, and often for density estimation: estimating the probability density function of the underlying variable. A histogram is designed for large quantities of data. Groups of data are placed into bins.

Practice Problems:

1) Using their cosmic ray detector, teachers in the University of Rochester QuarkNet Center take counts of incident muons per minute at a given location to see if they can get a good "average" value for that place. Over the next 20 minutes, the following counts are taken: {98, 103, 104, 103, 101, 98, 99, 104, 100, 104, 98, 103, 105, 103, 102, 104, 104, 103, 99, 100}. Group the data into bins. Make a histogram using this data.

2) The following is a list of the amount of time (in minutes) that it takes various students to get to school by bus: {10, 14, 9, 14, 25, 45, 13, 21, 18, 12, 7, 16, 35, 30, 12, 26, 24,19, 11, 20}. Make a histogram using this data.

3) The following is a list of prices (in dollars) of candy found in various drug stores: {1.45, 2.20, 0.75, 1.23, 1.25, 1.25, 3.09, 1.99, 2.00, 0.78, 1.32, 2.25, 3.15, 3.85, 0.52, 0.99, 1.38, 1.75, 1.22, 1.75}. Using this data, make a histogram.

AYYYY LOUIS!! have fun doing this blog!

Skills 5, 6, 7

2.1 Displaying Distributions With Graphs
Counts- the total number
Rates- percents and proportions—easier to understand than numbers (easier for comparison)
Distribution-the way something is spread out among a group
Example—with a variable and how it is distributed, values of the variable and how often it uses each value
Round off errors- the difference between the approximated number and its exact value
Example 2.1—Education level in the United States: a bar graph
Bar graph- a diagram with variables which are represented by height and length of lines or rectangles of equal width
- Good visual method of comparing data
- Easier to do by hand—more accurate
Example 2.2—Education level in the United States: a pie chart
Pie Chart—a circle which is divided into parts which represent a percent of the whole
To make a pie chart you make a circle and, using a protractor to accurately show the angles, you fill in the percents given. If you are given a percent then you must convert it to degrees. A circle is 360 degrees so an example of converting percent to degrees would be:
If you were given 22.8% then you would do-- .228 X 360= 82
Example 2.3—Hang up and drive!
Even though you always have the option of using a bar graph you cannot always use a pie chart. For example in the experiment given they are testing the percent of people that use cell phones while driving in each region. Because regions are being used there is no whole, the experiment only compares four separate quantities.
Practice Problems—
(found on page 40)
2.1 Martial status—In the Statistical Abstract of the United States we find these data on the marital state of adult American women as of 2007


Marital Status Count (thousands)
Never Married 25,262
Married 65,128
Widowed 11,208
Divorced 13,210
Total 114,807


a) How many women were not married in 2007?
b) Make a bar graph to show the distribution of marital status.
c) Would it also be correct to use a pie chart? If so, make a pie chart for these data

2.2 Consistency? Refer to the previous exercise. What is the sum of the counts for the four marital status categories? Why is this sum not equal to the total given in the table?

2.3 College Freshman—a survey of college freshman asked what field they planned to study. The results: 25.2% arts and humanities, 19.3% business, 7.1% education, 16.6% engineering and science, 7.8% professional and 15.3% social science.
a) What percent plan to study fields other than those listed?
b) Make a graph that compares the percents of college freshman planning to study various fields.

You got the next blog Geoff! Congrats!

Skill 3

Skill Goal: Determine if a study is observational or an experiment

• An observational study observes individuals and measures variables of interest but does NOT attempt to influence the responses. The purpose of an observational study os to describe a group or situation.
• An experiment deliberately imposes some treatment on individuals in order to observe their responses. The purpose of an experiment is to study whether the treatment causes a change in the response.

Practice Problems

1. One study of cell phones and the risk of brain cancer looked at a group of 469 people who have brain cancer. The investigators matched each cancer patient with a person of the same sex, age, and race who did not have brain cancer, then asked about cell phones. Result: "Our data suggest that use of hand-held cellular phones is not associated with risk of brain cancer."

a) Is this an observational study or an experiment? Why?

b) What individuals are measured, and what variables are recorded?

2. My grandmother once told me that the color red makes bees angry. Here's a method I've designed to test her claim. I'll select half of my students (by drawing names from a hat) to wear re clothes and the other half to wear white clothes. Then I'll turn a bunch of bees loose in our classroom and see how many times each student is stung.

a) Is this an observational study or an experiment? Why?

b) If students wearing red clothes are stung much more often than students wearing white, can we conclude that the color causes bees to sting more? Why or why not?

3. Is there a relationship between physical fitness and leadership ability? To answer this question, researchers recruited 100 students who are willing to take part in an exercise program. The volunteers are divided into a low-fitnes group on the basis of a physical examination. All students then take a test designed to measure leadership, and the results for the two are compared.

a) Is this an experiment or an observational study? Explain your answer.

Answers

1. a) This study is an observational study because nothing was done to the cancer patients that influenced the results of the study. The cancer patients were just matched with non- cancer patients and asked a series of questions.

b)Cancer Patients and Non-Cancer Patients are the individuals being measured. Their usage of cell phones is the variable.

2. a) This is an experiment because each student was assigned a specific color to wear.

b) Yes we could conclude that based on the grandma's claim or we could disagree based on the fact that other things could aggravate a bee making it sting a student.

3. This is an observational study because no treatment was imposed on the two groups.

Main difference between the an observational study and an experiment: In order for a study to be experimental you have to DO SOMETHING or MANIPULATE the individual otherwise it is observational.

CONGRATULATIONS! Margot, I have chosen you to do then next blog!

Skill 2

Skill 2

- Observational Study: An observational study observes individuals and measures variables of interest but does not attempt to influence the responses. The purpose of this study is to describe some group or situation.

Observational studies have a population and sample. A population in a statistical study is the entire group of individuals about which we want information. A sample is a part of the population from which we actually collect information, which is used to draw conclusions from the whole.

Population and Samples Example Problem:

1.7 For each of the following sampling situations, identify the population and the sample as exactly as possible.

(a) A furniture maker buys hardwood in large batches. The supplier is supposed to dry the wood before shipping. The furniture maker chooses five pieces of wood from each batch and tests their moisture content. If any piece exceeds 12% moisture content, the entire batch is sent back.

Answer: So in this situation the population is all the batches of wood being shipped because it is the entire group that we want information from. The sample would be the five pieces of wood that are selected from each batch because this is the portion of the entire population that we are gathering our information from. The sample then tells us information about the whole.

(b) An insurance company wants to monitor the quality of its procedures for handling loss claims from its auto insurance policyholders. Each month the company selects a sample from all auto insurance claims filed that month to examine the accuracy and promptness with which they were handled.

Answer: The population in this case would be all the claims filed with the insurance company within a given month. This is because it is the entire group we want information from. The sample is the selected claims for that month, because again, it is the portion of the whole that we are gathering information from.

-Census: A census is a sample survey that attempts to include the entire population in the sample. So it is like an observational study that includes everyone in the population.

Key Point: A census is not full proof. A census can only attempt to sample the entire population. The Census Bureau for example estimates that the 1990 census missed 1.6% of the American Population.

Link to the 2010 census: http://2010.census.gov/2010census/

The link has all sorts of information about the 2010 census including a more detailed explanation of what it is.

-Experiments: An experiment deliberately imposes some treatment on individuals in order to observe their responses. The purpose of an experiment is to study whether the treatment causes a change in the response. So this is different from a census and an observational study because in an experiment you want a change in behavior.

Experiment Example Problem:

1.13 Before a new variety of frozen muffin is put on the market, it is subjected to extensive taste testing. People are asked to taste the new muffin and a competing brand and to say which they prefer. Is this an observational study or an experiment? Explain your answer.

Answer: This is an experiment because a treatment is imposed on the subjects. The subjects are the people and the treatment would be the new muffin. The person running the experiment is influencing the result of the experiment. The subject is being given a new muffin which will influence the subject's responses.

In conclusions, observational studies, census', and experiments are just different methods of analyzing and collecting data.

Skill 1

Individuals

- Whatever you’re getting information about

- (The Categories and People)

Variable

-Numerical

-Categorical

__

Example Problem 1.2

How do you find out who recycles more?

- Quantity

- group --> quantity ( middle class trash weighs less, so you can't measure by weight)

- equivalence (One wine bottle = ? amount of soda cans)

- amount of recyclable purchases to the percent of those things recycled

-assign a value to the numbers on the recycled materials

_____

*Coming up with a question and figuring out the best way to prove or disprove what your question asked, is the basis of statistics

*Is it categorical or numerical? Some can go both ways.

EX. Sports Teams (# of sports teams OR types of sports teams)

_____

http://www.internetworldstats.com/stats.htm *good website for statistics of most everything. Bar graphs that can be used as categorical or numerical