Wednesday HW = More Comparing Boxplots

Tonight please complete the "AP Statistics: Comparing Boxplots" worksheet provided in class (or below).

• First, create the boxplots! You can't use your L1 and Stat Plots here because we don't have the full data set, so you'll have to create these by hand--you have notes about this from day two of our summer academy!
• Be as precise as possible when drawing your boxplots!
• After you create your boxplots, compare! Use the example from Monday/today's class/notes as a guide; you can also use last night's homework as a guide. I would score this comparison using the same rubric as last night's homework!
• The correct boxplots are shown below --check these! Be sure you have the correct boxplots before you start to compare!

Correct Boxplots for HW:

Today's Class Recap:

• Finished our "comparing boxplots" example with the puzzle completion times by adding some examples of comparative "% statements" (see the blog post from Monday and/or Tuesday for the full written comparison)
• Started chapter 6 = new stuff!
• Discussed shifting and rescaling...
• Definitions of each
• How does shifting affect measures of position (including center) and spread?
• How does rescaling affect measures of position (including center) and spread?

Tomorrow it's on to more chapter 6 notes; we'll look at some shifting/rescaling problems/examples in our chapter 6 slides, then we'll start to get into z-scores (and hopefully the Normal model). See you there!

Thursday's (tentative) HW (if you're curious and want to try some tonight):

Page 123: 1, 3, 5, 7, 9, 11

HW Due Weds (scroll down) AND Monday's Notes

If you were absent today you must make up the test before the end of the day Friday (I will not be after school Friday):

• You can do this during any free period or lunch
• Or I will be after school Wednesday or Thursday until 3:00 (come right at 2:10)
• I would not suggest making up the test during our class period--then you'll miss the stuff we learn in class!

Here is a recap of Monday's notes/example: Comparing Boxplots-- Use this to help with the HW due tomorrow!

• Period E: you must finish these notes (copy this example in blue) on your own since we didn't get far enough in class!
• I tried to write these bullets so that you can use the same structure for your homework--but for your homework you'll need to change everything that's underlined to the context about graduation rates and to the correct comparative language!
• First bullet = shape, outliers
• Next bullet = comparing center, interpreting what this means in context
• Third bullet = comparing spread, interpreting what this means in context
• Last bullet = comparing overall context with a % statement
• Our stamp problem on Wednesday will focus on this type of "% statement," and we'll come up with some options for this example for that warmup
• The distribution of puzzle completion times (time it took to complete a series of brain teasers) is skewed right with one outlier for females and roughly symmetric with no outliers for males.
• The females had a lower median puzzle completion time than the males -- this suggests that females generally completed the puzzles faster than the males.
• Males had a wider/larger IQR than the females -- this suggests that puzzle completion times varied more in the middle 50% for males.
• Overall, females completed the puzzles faster. Roughly _____% of females completed the puzzles faster than (at least ___% of males)

HW Due Tomorrow:

1. Answer the question! Compare the distributions! Give a real, thoughtful effort--write your answer as you would/should on the AP exam! Use the example above and your notes from Monday!
• You should be able to compare shapes, center, and spread, with context
• Don't forget, after you compare centers/spread add a "-- this suggests..." statement.
• Do your best for the "% statement"-- we will discuss this in more depth tomorrow to start class
2. Check out the rubric/grading breakdown on the back to score yourself!
3. Save this! We will definitely have a question like this on our end-of-unit test in a couple weeks!

STUDY. STUDY. STUDY. STUDY. STUDY. STUDY. STUDY.

Tomorrow's the big day--chapter 5 vocab quiz (8-10 min) AND chapter 2/4/5 test! (35 min)

• Come ready! Not only do you have to know the content, but you have to know it well enough to work quickly!
• Come right to class and immediately get to work! You can start before the bell for a little extra time, but you have to finish by the end of the period!
• Study. study. study. Did I mention you should study?

• Here's your vocab list for the chapter 5 vocab quiz:
• Some of these were on our chapter 4 vocab quiz!
• Center (from ch. 4 quiz)
• Measures of center (know which statistics are measures of center)
• Mean
• Median
• Midrange
• Spread (aka variability) (from ch. 4 quiz)
• Measures of spread (know which statistics are measures of spread)
• Range
• Interquartile Range (IQR) -- know what it is and how it's calculated
• Standard Deviation -- know what it is (definition)
• Variance -- know what this is, based on standard deviation
• Percentile
• First Quartile/Lower Quartile/Q1
• Third Quartile/Upper Quartile/Q3
• Histogram
• Boxplot
• Ogive
• Stemplot
• Appropriate summary statistics
• Know which measures of center, spread are best for a skewed distribution
• Know which measures of center, spread are best for a (roughly) symmetric distribution

• And here's an outline of (some of) the content to study for the open ended "math" part of tomorrow's test:
• Identify a given variable as categorical or quantitative 
• Look over your "analyzing context" quiz or homework from chapter 2
• Find probabilities from a 2 way table
• Look at last night's Titanic homework (answers below), or the driver age/ticket context from day 3 of our summer academy
• Determine if two variables are independent (not related) or not independent (related) based on probabilities
• Back to that Titanic homework and/or the day 3 summer academy notes
• Identify the explanatory (IV) and response (DV) variables for a given context
• Look at your summer assignment--the first page with the ice cream sales context, or there's a multiple choice about this later in the packet
• Read/analyze a histogram--determine sample size, estimate median, estimate range
• Look at the very first warmup from day 1 of our summer academy about college debt
• You also have a stamp half sheet about the lengths of Greek tragedies with these types of questions
• OR there's more of this on the back of your Chips Ahoy quiz!
• Determine if a given study is an experiment, observational study, or sample survey
• Check out your chapter 2 notes--you have notes describing each of these methods of data collection, and how to recognize each
• This is also the last question on our "analyzing context" quiz from chapter 2
• Describe a distribution given a boxplot and/or histogram
• You have lots of examples of this! Look at the "Old Faithful eruptions" or "Customer Service wait times" examples, or we did plenty of these in our textbook and you were given a typed up key
• Look at the AP free response about tip amounts, part a
• Look at your notes from Friday where we described a distribution given a boxplot (ESPN employee lunch costs). DEFINITELY look over this...
• Given boxplots be able to compare summary stats
• This is NOT like the write-up we had today (we'll finish that Wednesday)
• Instead, look at your homework about sleep times--given some boxplots be able to identify the highest/lowest median, widest/most narrow IQR or range, highest/lowest Q1/Q3/max/min, etc.
• Determine if a data set has outliers given the 5 # summary
• Fences! Use your notes from day 2 of the summer academy, or you have more of this in chapter 4
• This is also the first 2 questions on the AP/SAT classwork we had when I was absent
• Know how to draw a boxplot by hand
• Day 2 summer academy notes again!
• I think we also have an example with the movie ticket sales context in our chapter 4 notes where you are given a table with values below Q1, Q1, Median, Q3, and values above Q3
• Determine shape from a 5 # summary and/or boxplot
• See Friday's notes and today's stamp problem
• Know how mean and median relate (which is higher/lower) for a given shape of a distribution
• Look at your chapter 5 notes for more on this
• Know how changing a data value may affect various summary statistics
• Look at the free response question about tip amounts, part b, where we changed a tip amount from 8 to 18--this question asked how such a change would affect the mean and median, but also consider how it would affect range, IQR, standard deviation, and midrange
• Or look at the multiple choice that's on the homework we had with the 2012 free response about household sizes
• Find an overall mean when combining samples
• Day 3 of our summer academy notes, first example
• Or look at the first multiple choice on the stamp you got passed back today that had 3 questions on it

Answer Key to Last Night's Homework;

• Comparing Boxplots:
• 1.) Seneca has the most variability in its grape prices because it has the largest/widest range and also has the largest/widest IQR (tied with Cayuga for largest IQR).
• 2.) Keuka generally has the most grapes because it has the highest median, highest Q1, and highest Q3. .
• Approximately 75% of the grapes from Keuka were more expensive than at least 75% of the grapes from Cayuga and Seneca.
• All but one of the grape prices at Keuka were higher than at least 75% of the grape prices at Cayuga and Seneca.
• Titanic
• a.) 203/711 = 0.286
• b.) 203/325 = 0.625
• c.) 203/2201 = 0.0922
• d.) 325 + 711 - 203 = 833; 833/2201 = 0.3785
• e.) 711/2201 = 0.323
• f.) 203/325 = 0.625
• g.) **Should have said 'based on e,f above**
• Based on e and f, survival and class on the Titanic are NOT independent because first class passengers had a higher (almost double) chance to survive than a randomly selected passenger. 
• OR...
• Survival and class on the Titanic are related because first class passengers have a higher chance of survival than the chances of survival overall.
• Note: DO NOT comment on the chances of survival for a first class passenger to the chances of survival for the other classes--we did not calculate the chance of survival for the other classes (in e,f), and the question clearly states that we should use our answers to e,f to make our decision.

Today's Comparing Boxplots Notes/Example -- Use this to help with the HW due Weds!

• I tried to write these bullets so that you can use the same structure for your homework--but for your homework you'll need to change everything that's underlined to the context about graduation rates and to the correct comparative language!
• First bullet = shape, outliers
• Next bullet = comparing center, interpreting what this means in context
• Third bullet = comparing spread, interpreting what this means in context
• Last bullet = comparing overall context with a % statement
• Our stamp problem on Wednesday will focus on this type of "% statement," and we'll come up with some options for this example for that warmup
• The distribution of puzzle completion times (time it took to complete a series of brain teasers) is skewed right with one outlier for females and roughly symmetric with no outliers for males.
• The females had a lower median puzzle completion time than the males -- this suggests that females generally completed the puzzles faster than the males.
• Males had a wider/larger IQR than the females -- this suggests that puzzle completion times varied more in the middle 50% for males.
• Overall, females completed the puzzles faster. Roughly _____% of females completed the puzzles faster than (at least ___% of males)

HW Due Weds:

1. Answer the question! Compare the distributions! Give a real, thoughtful effort--write your answer as you would/should on the AP exam! Use the example above and your notes from Monday!
2. Check out the rubric/grading breakdown on the back to score yourself!
3. Do this tonight to help you study!

Weekend HW!

This weekend please complete the Comparing Boxplots/Probability and Two Way Tables practice provided in class (or below--no excuses)!

• For the comparing boxplots questions (a and b): WRITE YOUR ANSWERS IN COMPLETE SENTENCES, IN CONTEXT!
• For (a) remember that variability is just a fancy word for spread--you should reference two statistics here to explain why whichever region has the most variablility.
• For (b)--here, you should reference some summary statistics AND should make at least one statement COMPARING percentages
• Remember to use comparative language throughout: higher/lower, bigger/smaller, etc!
• For the back (the Titanic probability questions you should show a fraction (your work) and write your final answer for each solution. Probabilities should be written in decimal form for our final answer. 

Do yo homework! On Monday we'll spend our class focusing on how we compare boxplots--and then it's test time on Tuesday!

Weds HW (Due Friday)

Vote for a math shirt--check out the poll/image on the right--nevermind. Due to technical difficulties we will do this in class tomorrow.

• There is a school wide vote to narrow down the design for an EHHS math shirt; these shirts will be dry-fit, uniform approved shirts that can be worn any day of the week!
• They will cost $15 for a short sleeve, $20 for long sleeve
• All shirts will be black and gold (not the colors in the picture)

Homework due Friday -- please complete the following in your textbook:

Page 91: 5, 7, 17, 27de, 29cd, 35abc, 37de

• For any question that asks what measure of center/spread you should use then consider the shape--and when you explain your reasoning, the explanation is short--simply something like, "We'd use the median/IQR because the distribution of ____ is skewed left/right."
• For #5 you're not calculating anything--your job is to determine what would happen to each summary statistics--would they increase, decrease, or stay the same? Why?
• Assume the boss' salary is the maximum (thanks for pointing that out Tahlea)
• For 7cd and 17 consider the "appropriate summary statistics" info we discussed today in class!
• For 27de consider today's notes about spread!
• I know we've looked at 29ab before--revisit this question and try to be more specific, use specific stats vocab (you don't necessarily have to write anything, but think about this!)
• For 29cd--back to "appropriate summary stats"-- and the "why" is simply referencing the shape of the distribution!.
• For 37d you need to use the 5 number summary to try to decide if this is skewed or symmetric (we can't figure out the modality from this info)--consider our notes on describing the shape of a boxplot!
• For 37e be sure to reference these summary statistics as your support when you "explain." Try to comment on percentiles with statements "___% of boys/girls had a higher reading level than ___% of boys/girls."

Extra Credit Homework: Sample Responses

• Remember, describe Shape, Outliers/Gaps, Center (median), and Spread (range), then make a "Generally..." statement commenting on the cluster
• ALWAYS WRITE EVERYTHING IN CONTEXT!
• If we do these things our answer will always be "essentially correct!"

1.) The distribution of the ratio of the number of pupils to the number of teachers for 24 states west of the Mississippi is unimodal and skewed right, with no apparent outliers. The median ratio of the # of pupils to the # of teachers is between 15 and 16. The range of the pupil to teacher ratio is approximately 10. Generally, the ratio of the # of pupils to the # of teachers for states west of the Mississippi was between 13 and 18.

2.) The distribution of the ratio of the number of pupils to the number of teachers for 26 states east of the Mississippi is unimodal and roughly symmetric, with no apparent outliers. The median ratio of pupils to teachers is roughly between 15 and 16, with a range of about 7. Generally, the ratio of the number of pupils to the number of teachers in states east of the Mississippi is between 13 and 17.

I'll leave you with this classic....

Hump Dayyyyyyyy

Tuesday HW!

Tonight there is no assigned homework! But you should put in some work...

1.) Take the time to look over the sample responses for describing the distribution of the number of chocolate chips per bag of Chips Ahoy cookies--I'd even recommend copying one down (not the one with the incorrect histogram) on your quiz--this will help you to retain this info more, and will force you to compare your response to a perfect one as you copy!

2.) Want more practice describing distributions? How bout a little extra credit homework--this will only be accepted tomorrow!

Homework due Friday -- please complete the following in your textbook:

• If you're looking to get a head start you can probably do some of this tonight, like some of #5, 27de, and 37e

Page 91: 5, 7, 17, 27de, 29, 35abc, 37de

• For #5 you're not calculating anything--your job is to determine what would happen to each summary statistics--would they increase, decrease, or stay the same? Why?
• For 7cd and 17 consider the "appropriate summary statistics" info we discussed today in class!
• For 27de consider today's notes about spread!
• I know we've looked at 29ab before--revisit this question and try to be more specific, use specific stats vocab (you don't necessarily have to write anything, but think about this!)
• For 27cd--back to "appropriate summary stats"-- and the "why" is simply referencing the shape of the distribution!.
• For 37d you need to use the 5 number summary to try to decide if this is skewed or symmetric (we can't figure out the modality from this info)--consider our notes on describing the shape of a boxplot!
• For 37e be sure to reference these summary statistics as your support when you "explain." Try to comment on percentiles with statements "___% of boys/girls had a higher reading level than ___% of boys/girls."

Tomorrow in class we'll finish talking about standard deviation, discuss some ogives and how to compare boxplots--then Friday we'll do some work with comparing distributions and we'll revisit that free response--see you there!

Monday HW + AP FR

1.) Tonight, please complete the following in your textbook:

Page 91: 11bcd, 27abc, 37abcf

• See below for #11....
• For 11b consider today's stamp!
• 11c is another opportunity to be sure you know how to calculate the 1 var stats--if you KNOW this already, feel free to just get the median and IQR from the back of the book
• 11d = more describe a distribution practice!
• For 27ab this can be tricky--consider where most of the data falls, and remember, even if the mean is less than the median within one data set, that doesn't necessarily mean that the average (mean) is less than that of another data set...
• For 37abc use the 5 # summary!
• 37f = summer review! Be sure you know how to do this--use your notes from day 3 of the summer academy. 

2.) If you didn't do so already, COMPLETE AND SCORE the AP MC and AP FR question provided in class on Friday--I will also check this in class tomorrow.

• Read the directions!
• For the AP MC be sure to write a bullet/notes about how each summary statistic
• For the free response be sure to COMPLETE and SCORE the free response!
• You have to look at the sample response to see the correct answers--for instance, you have to comment on shape correctly! The rubric may only tell you to comment on the shape, the sample response is where you can see that the shapes are both skewed right!
• Here is the link to the AP scoring rubric:
• 2012 Scoring Rubric (scroll to question #3)
• And here are the questions:

Tomorrow in class we'll talk more about spread (standard deviation), and maybe some ogives; then, on Wednesday, we'll start to describe some boxplots, and we'll spend Friday focusing on comparing distributions. 

Here are some of the "big picture" goals for the coming weeks:

1. Finish chapter 5 Monday with a full period quiz (or more like a "quest") on Tuesday 9/25 covering everything we've learned thus far.
2. Finish chapter 6 from 9/26 to 10/5 with our two unit tests (vocab test, AP FR/MC test) completed by 10/10