Graphs and standard deviation & CiCi's

Preparing for the test
Your test is Thursday. Begin to prepare now by working problems and creating an outline.

Homework: For those in class today - rewrite your responses to the FR questions, plus work problem 1.4 from the text.

For those absent today: Problem 1.4 PLUS ALL OF 1.48-1.52. Pick up your original responses to the FR upon your return to complete overnight. If you were participating in Senior Skip Day, your absence is unexcused.

CiCI's
YES!!!! There is a request for CiCi's this Sunday, so I will be there from 2 to 4. That is the one by the Walmart at Trickum and 92 (close to Arby's).

Test is Thursday, 9/6!

If you are going on the marketing fieldtrip, stay after school to take the test in room 214 at 3:30. Don't forget to bring your calculator.

For Tuesday (9/4), select one odd and one even problem from the set 1.48-1.52 and work them completely. Become an expert on one of the problems.

For Friday (8/31), complete problems 1.41 and 1.43. The answers are in the back of the book, but that is not sufficient! You must show all work and explain your actions.



By Thursday (8/30), you should have both the graph from the Internet, a newspaper, or magazine and problems 1.35 and 1.36 from the text.

RE: the graph
You will identify the variable(s) represented in the graph and the type of graph you brought. Are the data numerical or categorical? Are numerical data discrete or continuous? Does your graph represent one variables or two? Is a trendline appropriate for your data?

RE: Standard deviation

The standard deviation of a sample of data is like an average deviation from the sample mean. It is the square root of the sample variance, which is an unbiased estimator of the population variance.

If we just found the sum of the deviations, we would get a sum of zero because some data are above the mean and some are below. Because of the definition of the mean, the positives and the negatives cancel each other out.

Instead, we square each deviation so the numbers we add together are all positive. We "average" these numbers by dividing by (n-1). You remember that n is the number of observations. We subtract one because we are using an estimate derived from the data themselves for x-bar. This gives us the sample variance or s-squared. To get the value of s just take the square root.

In formula form, s = sqrt(sum of all the squared deviations/(n-1)). The formula for the first squared deviation is (x minus x-bar)^2. Again, x-bar is the average of the x values.

The same relationship holds between sigma and sigma squared, the population standard deviation and the population variance: you take the square root of the variance to get the standard deviation.

Cumulative and relative frequency histograms

We created cumulative frequency histograms and relative frequency histograms today. For the cumulative frequency histograms, find the cumulative sum up to and including each line of the frequency table, for instance,

x freq cumulative freq
1-5 4 4
5-10 5 9
11-15 6 15


For the relative frequency distribution, divide the count for an interval by the total number of observations, n. What do you observe about the graphs of frequency and relative frequency????

The HW is attached to the site at classhomework.com.

Histograms - a beginning

Find a nice set of data to graph.

Create a frequency table for the data, breaking the data into 5, 7, or 9 intervals of equal length. That does NOT mean that there will be an equal number of observations in each bin or interval!

Create a histogram to represent the data.


http://www.ncsu.edu/labwrite/res/gt/gt-bar-home.html in Excel

http://jwilson.coe.uga.edu/EMT668/EMAT6680.F99/Estes/graphicaldisplays1page.html on the TI-83, but you need to reset the window!!!


http://facstaff.colstate.edu/henning_cindy/Calculator%20Assistance_files/Creating%20Histograms%20on%20TI83.htm

Stem and leaf plots

Create a stem-and-leaf graph (a stemplot) of your data. If your data your data don't go nicely into a stemplot, find some fun data to use instead.

More later. . .


Have you found good resources on the web?


Do these help?
http://regentsprep.org/regents/math/data/stemleaf.htm

http://en.wikipedia.org/wiki/Stemplot

http://www.sjsu.edu/faculty/gerstman/StatPrimer/freq.pdf

More box and whisker

Using the data from problem 1 of the 2001 exam, answer the questions posed in class. Part C reads, "The news media reported that in a particular year, there were only 10 inches of rainfall. Use the information provided to comment on this reported statement.

Keep in mind all the errors that students might have made under test conditions. What do you suppose that a student under extreme time pressure might have done wrong on this problem?

Box and whisker plots

You collected data today in class and we talked through the processes of finding the five number summary and constructing a box and whisker plot for univariate quantitative data.

5 number summary: Min, Q1, Med, Q3, Max

Use the 5 number summary to construct the box and whisker plot. Use the interquartile range (the length of the box containing the middle 50% of the distribution)to determine whether observations are outliers. The boundaries of reasonable answers are Q1 - 1.5(IQR) and Q3 + 1.5(IQR).
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For homework, construct the modified box and whisker plot for your data.
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There are many websites that explain how to perform this task.
http://www.statcan.ca/english/edu/power/ch12/plots.htm

Can you find one that you like better? Please share the site with the rest of us.

Types of variables

You further analyzed the data you collected last week and made a claim about whether we can use the x-value to predict the y-value for your experience.

We discussed many types of variables in class today, focusing on quantitative (discrete and continuous) and categorical.

Create a list of 20 clever variables and identify whether each is quantitative or categorical. Include both types in your list. If the variable is quantitative, determine whether it is discrete or continuous.

Examples:

The number of students in math classes at Lassiter: quantitative and discrete.
The number of minutes of studying/homework done by students each night: quantitative and continuous.
The math course taken by students at Lassiter: categorical. [The values that the variable can take are the different courses.]

The linear labs

Find the least-squares regression line through the data you collected in class today. Describe trends in your data, the direction, linearity, strength of the relationship, and presence of outliers. Present a comment about the nature of the connection between the x and y values from your lab.

First period:

These may not be your actual data. . . the postits got a little mixed up. Anyway, you can use these for your HW.


Other classes:
If you lost your data, post a message asking for your particular set of data. NO LAST NAMES PLEASE!!!!


Arm/foot
12, 10.5
11, 10
11, 9.5
11, 10
11.5, 10
11, 10
11, 10
11.5, 10.25
12, 10.5
11.5, 10
12, 11.5
11.5, 10
11, 9
10, 8.5
9.5, 9.25
11, 9
8.5, 9
8.5, 9


Days
15, 16
1, 30
3, 28
9, 21
8, 22
12, 18
11, 17
14, 17
15, 16
17, 14
19, 12
7, 23
26, 5
24, 7
25, 6
24, 6
30, 1
30, 1

Ball toss
5, 6
3, 3
3, 3
2, 4
1, 2
2, 1
1, 0
0, 0

The ball-measurement lab

You did a good job using the center, shape, and spread of data to match the graphs to the summary statistics for last night's assignment.

The data you collected will be posted here. Please post comments and questions attached to this entry. Our technical team is standing by, ready to answer your questions!

Your assignment is to generate a least-squares regression line for the data. Your technical team will post instructions.

Do not use your full name when you create your account.

Here are data you collected:

Circumference Diameter
25 3.5
24.75 3.5
19.5 2.5
19.875 3.25
19.75 3
19.75 2.5
20.5 3
16.5 2.25
16 2
15.25 2
12.25 1.5
15.25 2
8 1
8.5 1
12 1.5
12.5 1.75
8.25 1.25
12 1.75
13 1.75
5.5 0.75
3.5 0.5
5 0.5
3.5 0.5
5.5 0.75
4.75 0.5
5.5 0.75
9 1.25
12.5 1.75
15.25 2.25
20 3
19.75 2.5
25 3.5
9 1.25
12.2 1.75
8 1
5.5 0.75
4.75 0.75
8.25 1.25
20 5.5
33 8.5

Welcome to the new school year!

You did a marvelous job of spinning pennies today. Can you think of ways to minimize the outside influences on the results of the spin? How could you make the results dependent only on the fairness of the coin--well, as much as possible?

Your homework can be found on Classhomework.com.

Some of our classmates have reported that the composition notebooks are sold out of local stores. Don't panic. We won't do our first write-up for at least another week.

Also, don't rush out to buy a study guide or a new calculator. The new edition of the Barron's guide will be released in September. TI will be releasing the new calculator, the TI-Inspire in September as well. There is no sense in spending money on last-year's model.

We will issue textbooks when we finally need them. We will do some more investigations (labs) in class before we use the text.

When you (eventually) need to retrieve a document from the HW website, the password that you will use is lassitermath.

Leave a comment if you want to share thoughts or questions.