AP STATISTICS SUMMER 2013 ASSIGNMENT - L. Banks' Blog

AP STATISTICS SUMMER 2013 ASSIGNMENT The first unit of AP Statistics begins with the basics of descriptive statistics. Many of these concepts have been covered in previous math and science courses. Over the summer you will review these topics and complete this packet. Writing and reading comprehension are important components to the course. At the end of this packet are four tasks that require you to explain your reasoning/responses. Listed below are some Internet sites that contain information about descriptive statistics. www.mste.uiuc.edu/hill/dstat/dstat.htm www.habermas.org/stat2f98.htm http://www.khanacademy.org/#statistics The following packet is due at the first meeting of AP Statistics. This will be graded as the first homework assignment. This assignment will be grade based upon the following: 1. completeness of work. 2. consideration of correctness of answer Upon your return to school in August, there will be a quiz on the concepts included in this assignment.

Created By: L. Banks, Arabia Mountain High School

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Suggested Summer Reading List There are many good books that deal with deep statistical ideas without getting too technical. It is highly recommended that you choose at least one of the following books to read during the summer.                    

Outliers, by Malcolm Gladwell. Little, Brown, & Co 2008 Innumeracy, by John Allen Paulos. Hill and Wang Freakonomics: A Rogue Economist Explores the Hidden Side of Everything, by Levitt & Dubner. HarperCollins, 2005. A Mathematician Reads the Newspaper, by J. A. Paulos. Basic Books, 1995. The Lady Tasting Tea, by D. Salsburg. Owl Books, 2001. 200% of Nothing, by A. K. Dewdney. John Wiley and Sons, 1993. Moneyball: The Art of Winning an Unfair Game, by M. Lewis. Norton, 2003 (tells how the Oakland A’s revamped their baseball team using basic stats) Bringing Down the House: How Six Students Took Vegas for Millions, by Ben Mezrich (Breaking Vegas & "21" movie are based on this book). Free Press Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets, by N. Taleb. Thomson, 2004 How to Lie with Statistics, by D. Huff. W. W. Norton, 1952. The Black Swan: The Impact of the Highly Improbable, by N. Taleb. Thomson, 2007 Damned Lies and Statistics: Untangling Numbers from the Media, Politicians, and Activists, by J. Best. Univ of California Press, 2001. More Damned Lies and Statistics: How Numbers Confuse Public Issues, by J. Best. University of California Press, 2004. The Drunkard's Walk: How Randomness Rules Our Lives by Leonard Mlodinow. Pantheon Books, 2008 Tainted Truth: The Manipulation of Fact In America, by C. Crossen The Ghost Map: The Story of London's Most Terrifying Epidemic—and How It Changed Science, Cities, and the Modern World, by S. Johnson A Cartoon Guide to Statistics, By L. Gonick & W. Smith. Harper, 1993 The Tipping Point: How Little Things Can Make a Big Difference, by M. Gladwell, Little, Brown & Co., 2002 Calculated Risks: How to Know When Numbers Deceive You, by G. Gigerenzer. Simon and Schuster, 2002 The Universe and the Teacup: The Mathematics of Truth and Beauty, by K.C. Cole


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Name _______________________________________________ Period _______________

Part I. Measuring Central Tendency a. Find the mean, median, and mode of the following data set: 15, 11, 19, 15, 14, 13, 17, 11, 12, 17, 15, 14, 15, 14 To begin, order the fourteen numbers: 11, 11, 12, 13, 14, 14, 14, 15, 15, 15, 15, 17, 17, 19 To find the mean, divide the sum of the numbers by 14. 2 11

12

13

3 14 14

4 15

2 17

19

14.4

The mode is 15 because that is the number that occurs the most frequently in a data set. The median is the average of the two middle number for a data set with an even count of numbers. 14 15 14.5 2 For a data set with an odd count of numbers the median is the middle number. b. Find the quartiles of the data set from example a. ,

,

,

,

,

,

,

lower half

,

,

,

,

,

,

upper half

First, divide the data set into two equal halves, called the lower half (values less than the median) and the upper half (values more than the median). The first and third quartiles (Q1 and Q3) are the medians of the lower half and upper half, respectively. For the data set in example ‘a’, Q1 = 13, and Q3 = 15. c. Find the range of the data set from example a. The range is the difference of the highest (maximum value) and lowest (minimum value) data values in a data set. For the data set, 19

11

8


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d. Sketch a box-and-whisker plot of the data set from example a. A box-and-whisker plot of a data set labels the endpoints of the data set and marks the quartiles and the median of the data set. For now, don’t worry about the “height” of the box, labeling the correct points should be your focus. A box-and-whisker plot of the data set from example a: Median Q1

Q

Maximum

Minimum

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Exercises 1. Find the mean, median, mode, and range of the following collection of scores on a test. 32, 72, 81, 95, 98, 58, 77, 75, 83, 97, 45, 89, 93, 57, 82, 97, 52, 75, 79, 78, 99, 98, 54, 75, 85, 61, 55, 86 2. Find the first, second, and third quartiles of the data set in Exercise 1. 3. Construct a box-and-whisker plot of the data set in Exercise 1. 4. Complete #1-3 for the following set of data. The weights (in pounds) of eleven children are as follows: 39, 52, 40, 45, 46, 55, 48, 40, 43, 47, 44


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Part II. Organizing Data At a car dealership, the number of new cars sold in a week by each salesperson was as follows: 5, 8, 2, 0, 2, 4, 7, 4, 1, 1, 2, 2, 0, 1, 2, 0, 1, 3, 3, 2 a. Construct a frequency distribution for this data. Number 8 7 6 5 4 3 2 1 0

Tally | |

Frequency 1 1 0 | 1 || 2 || 2 |||| | 5 |||| 4 ||| 3

b. Construct a line plot for this data (please use a straightedge).

c. Construct a bar graph that shows the number of salespeople who sold 0 – 8 cars (please use a straightedge).

Exercises 1. Twenty-eight students in a class were asked how many cars their family owned. The results were as follows: 2, 2, 3, 2, 1, 2, 2, 4, 3, 2, 0, 1, 0, 1, 1, 2, 2, 3, 2, 3, 3, 5, 1, 1, 3, 0, 1, 2 Construct a frequency distribution and a line plot for this data. 2. Each of the members of a recent high school graduating class was asked to name his/her favorite among these subjects: English, foreign language, history, mathematics, science. The results are shown in the table. Construct a bar graph that shows these results.

English Foreign Language History Mathematics Science


62 40 40 18 33

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Part III. Constructing Stem-and-Leaf Plots and Histograms a. Construct a stem-and-leaf plot (stemplot) for the following data set: 63, 52, 84, 83, 51, 32, 58, 35, 45, 41, 65, 75, 59, 67, 25, 46 To make a stemplot: 1) Separate each observation into a stem, consisting of all but the final (rightmost) digit, and a leaf, the final digit. Stems may have as many digits as necessary, but each leaf contains only a single digit. 2) Write the stems in a vertical column with the smallest at the top, and draw a vertical line at the right of this column. 3) Write each leaf in the row of its stem, in increasing order out from the stem. Stemplot of data set 2 5 3 2 5 4 1 5 6 5 1 2 8 9 6 3 5 7 7 5 8 3 4 b. Construct a histogram of the data set from example a. 1) Construct and label a horizontal line that is scaled to contain all of the values of the data set. 2) Construct and label a vertical axis so that the greatest frequency can be represented. 3) Construct the bars of equal width that are centered above each value. The heights of the bars represent the frequencies of the values.

Exercises 1. Construct a stem-and-leaf plot for the data 15, 59, 66, 42, 48, 23, 70, 81, 35, 51, 68, 29, 77, 92, 85, 16, 37, 59, 61, 76, 40, 25, 86, 11 2. Construct a histogram of the data from Exercise 1.


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Part IV. Using the TI-84/TI-Nspire Graphing Calculators For the TI-Nspire: *Note: All students will need to visit the websites below, even if you do not have access to a TI-Nspire at home. We will use the TI-Nspire throughout the course. A Texas Instrument graphing calculator is required for this course. As stated by The College Board, “students should have access to calculators both inside and outside the classroom.” Please visit the websites below for interactive tutorials. http://learningmedia.ti.com/public/media/EPS/tinspire/Statistics_Lesson2_Handheld.htm http://learningmedia.ti.com/public/media/EPS/tinspire/Statistics_Lesson4_Software.htm

For the TI-84: 1. Entering data into a list: STAT→ 1:Edit→ enter data in appropriate list 2. To clear a list: highlight the list name and hit clear. The list is empty when you see the dashes. 3. To sort a list in ascending order: STAT→ 2:SortA(L1) 4. To find the mean of a list: 2nd STAT→ MATH →3:mean(L1) 5. To find the median of a list: 2nd STAT→ MATH →4:median(L1) 6. To find the sum of a list: 2nd STAT→ MATH →5:sum(L1)

Exercises 1. 2. 3. 4. 5.

Enter the above data from Part III. Exercise 1 in a list. Sort the data in ascending order and find the mode. Find the mean of the data. Find the median of the data. Find the sum of the data.


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Tasks Task 1 Write two specific survey questions that you would ask voters in the next senatorial election in your state. Choose the type of question and response (yes/no, scale of 1 to 5, numerical responses, etc.) that would be most appropriate for the issues involved. What relationships would be expected when the responses are analyzed? Task 2 Find a set of numbers that will satisfy the following conditions:  The median of a set of 20 numbers is 24.  The range is 42.  To the nearest whole number the mean is 24.  No more than three numbers are the same. Show your strategy.


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Task 3 Two pain relievers, A and B, are being compared for relief of postsurgical pain. Twenty different strengths (doses in milligrams) of each drug were tested. Eight hundred postsurgical patients were randomly divided into 40 different groups. Twenty groups were given drug A. Each group was given a different strength. Similarly, the other twenty groups were given different strengths of drug B. Strengths used ranged from 210 to 400 milligrams. Thirty minutes after receiving the drug, each patient was asked to describe his or her pain relief on a scale of 0 (no decrease in pain) to 100 (pain totally gone). The strength of the drug given in milligrams and the average pain rating for each group are shown in the scatterplot below. Drug A is indicated with A’s and drug B with B’s.

a) Based on the scatterplot, describe the effect of drug A and how it is related to strength in milligrams. b) Based on the scatterplot, describe the effect of drug B and how it is related to strength in milligrams. c) Which drug would you give and at what strength, if the goal is to get pain relief of at least 50 at the lowest possible strength? Justify your answer based on the scatterplot.

Task 4 From the newspaper or magazines or the internet (mount the graphs on 11” x 14” poster board OR scan your articles into Microsoft PowerPoint, Word, or Publisher. Be sure to footnote/reference your article): a) Clip out an article that uses a bar graph, b) Clip out an article that uses a pie chart c) Clip out an article that use unscientific statistics from which the writer is probably making an inaccurate conclusion about what the data means. Write a paragraph explaining the defects in the story.


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