My Statistical Questions: I have a playlist on my iPod for when I go - PDF document

Best Fest Presentation.notebook August 01, 2015 My Statistical Questions: I have a playlist on my iPod for when I go running. A) How long are the songs in my running playlist? B) If I run for 40 minutes, how many songs might I get through if the songs are on shuffle? 6.SP.1, 6.SP.2 http://www.nctm.org/coremathtools/ Core math tools 1

Best Fest Presentation.notebook August 01, 2015 Fathom (software for teaching stats) http://fathom.concord.org The AP Stats teachers have this and there is a free trial available. Song lengths (in seconds) 2

Best Fest Presentation.notebook August 01, 2015 Data Distribution Data are the values assumed by the particular variable of interest. The distribution of this variable is the values of the variable together with the frequency of each value. "All possible values and how frequently" DRAFT Missouri Mathematics Core Academic Standards 6th Grade Glossary Dot plot A method of visually displaying of data values where each data value is shown as a dot or mark above a number line. Also known as a line plot. DRAFT Missouri Mathematics Core Academic Standards High School Glossary 3

Best Fest Presentation.notebook August 01, 2015 Histograms A graph that displays the data by using vertical bars of various heights to represent the frequencies of a distribution. The data is graphed in intervals. DRAFT Missouri Mathematics Core Academic Standards 6th Grade Glossary Song lengths (in seconds) 4

Best Fest Presentation.notebook August 01, 2015 Song lengths (in seconds) 6.SP.2, 6.SP.4, 6.SP.5 Song lengths (in seconds) 6.SP.2, 6.SP.4, 6.SP.5 5

Best Fest Presentation.notebook August 01, 2015 Song lengths (in seconds) 6.SP.2, 6.SP.4, 6.SP.5 Median A measure of center in a set of numerical data. The median of a list of values is the value appearing at the center of a sorted version of the list – or the mean of the two central values, if the list contains an even number of values. "The middle, when in order" DRAFT Missouri Mathematics Core Academic Standards 6th Grade Glossary 6

Best Fest Presentation.notebook August 01, 2015 Quartiles The value called the first quartile appears at the center of the lower half of a sorted version of a numerical list; the value called the third quartile appears at the center of the upper half of a sorted version of a numerical list. "The middle of each ordered half" Missing from the DRAFT Missouri Mathematics Core Academic Standards Box Plot A method of visually displaying a distribution of data values by using the median, quartiles, and extremes of the data set. A box show the middle 50% of the data. DRAFT Missouri Mathematics Core Academic Standards 6th Grade Glossary 7

Best Fest Presentation.notebook August 01, 2015 Interquartile range (IQR) A measure of variation in a set of numerical data, the interquartile range is the distance between the first and third quartiles of the data set "The spread of the middle half" DRAFT Missouri Mathematics Core Academic Standards 6th Grade Glossary Song lengths (in seconds) 8

Best Fest Presentation.notebook August 01, 2015 Song lengths (in seconds) 6.SP.2, 6.SP.4, 6.SP.5 Outliers Data that are more than 1.5 times the interquartile range from the quartiles. DRAFT Missouri Mathematics Core Academic Standards 8th Grade Glossary 9

Best Fest Presentation.notebook August 01, 2015 Song lengths (in seconds) 6.SP.2, 6.SP.4, 6.SP.5, S.ID.1, S.ID.2 Human Boxplot How many grandkids do you have? 1, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6 6.SP.2, 6.SP.4, 6.SP.5, S.ID.1, S.ID.2 10

Best Fest Presentation.notebook August 01, 2015 Human Boxplot How many grandkids do you have? 1, 1, 2, 3, 3, 3, 4, 4, 4, 5, 5, 6 Another person joins the group and that person has 9 grandkids. 6.SP.2, 6.SP.4, 6.SP.5, S.ID.1, S.ID.2 Roller coaster lengths (ft.) via rcdb.com A Worlds of Fun B Silver Dollar City C Six Flags St. Louis D Cedar Point 11

Best Fest Presentation.notebook August 01, 2015 Roller coaster lengths (ft.) A Worlds of Fun B Silver Dollar City C Six Flags St. Louis D Cedar Point 6.SP.2, 6.SP.4, 6.SP.5, S.ID.1, S.ID.2 Which month was busiest, based on email volume? Which month was hardest to predict what my inbox would look like from one day to the next? 6.SP.2, 6.SP.4, 6.SP.5, S.ID.1, S.ID.2 12

Best Fest Presentation.notebook August 01, 2015 Mean A measure of center in a set of numerical data, computed by adding the values in a list and then dividing by the number of values in the list. "Add them up and divide by how many" DRAFT Missouri Mathematics Core Academic Standards 6th Grade Glossary Mean absolute deviation A measure of variation in a set of numerical data, computed by adding the distances between each data value and the mean, then dividing by the number of data values. "The average distance from the mean" DRAFT Missouri Mathematics Core Academic Standards 6th Grade Glossary 13

Best Fest Presentation.notebook August 01, 2015 Standard deviation A measure of the dispersion (i.e., the degree to which data are spread out) of a set of data relative to the mean. "Another type of average distance from the mean" DRAFT Missouri Mathematics Core Academic Standards High School Glossary Song lengths (in seconds) mean = 339.73 Q1 = 241.5 median = 328 Q3 = 421.5 sample standard deviation (s) = 106.19 mean absolute deviation (MAD) = 88.75 interquartile range (IQR) = 180 6.SP.5, S.ID.2 14

Best Fest Presentation.notebook August 01, 2015 A tale of two data sets set 1 set 2 20 10 38 36 50 65 60 69 62 70 mean 50 50 range 60 60 22.85 26.37 sample standard deviation (s) mean absolute deviation (MAD) 16.8 21.6 6.SP.5, S.ID.2 Calculating Standard Deviation and MAD Four runners' distances for each of 5 days: Aaron Beth Caleb Donna 10 8 7 3 10 9 9 3 10 10 10 4 10 11 11 5 10 12 13 35 mean 10 10 10 10 s 0 1.58 2.23 14 MAD 0 1.2 1.6 10 6.SP.5, S.ID.2 15

Best Fest Presentation.notebook August 01, 2015 How changes in data affect statistics How many letters are in your first name? Lengths 3 Suppose Dan decides to 4 change his name to Daniel. 5 5 mean mean 5.14 5.57 median 6 median 5 6 s 6 1.35 s .98 7 MAD MAD 1.02 .78 range range 4 3 IQR 2 IQR 1 6.SP.5, S.ID.2, S.ID.3 How changes in data affect statistics How many letters are in your first name? Lengths 3 Suppose Chris decides to 4 change his name to Christopher. 5 mean 5 mean 5.14 6 median 6 median 5 6 s s 6 1.35 2.58 MAD 7 MAD 1.02 1.71 range range 4 8 IQR IQR 2 3 6.SP.5, S.ID.2, S.ID.3 16

Best Fest Presentation.notebook August 01, 2015 How changes in data affect statistics How many letters are in your first name? Lengths 3 Suppose a new student, 4 Jenna, joins the class. 5 5 mean mean 5.14 5.13 median 6 median 5 5 s 6 s 1.35 1.25 7 MAD MAD 1.02 .91 range range 4 4 IQR IQR 2 1.5 6.SP.5, S.ID.2, S.ID.3 How changes in data affect statistics How many letters are in your first name? Lengths 3 Suppose a new student, 4 Maximillian, joins the class. 5 mean mean 5.59 5 5.14 median median 5.5 6 5 s s 2.42 6 1.35 MAD MAD 1.63 7 1.02 range range 8 4 IQR IQR 2 2 6.SP.5, S.ID.2, S.ID.3 17

Best Fest Presentation.notebook August 01, 2015 Simulation A model of an experiment that might be impractical to carry out. DRAFT Missouri Mathematics Core Academic Standards 7th Grade Glossary 18

Best Fest Presentation.notebook August 01, 2015 Only 85 of the 1000 simulated shuffled playlists included an average of 6 songs taking longer than 40 minutes. 6.SP.4, S.ID.1, S.IC.2 Only 148 of the 1000 simulated shuffled playlists included an average of 8 songs in under 40 minutes. 6.SP.4, S.ID.1, S.IC.2 19

Best Fest Presentation.notebook August 01, 2015 Another simulation Suppose that at a certain company, 15 female employees and 10 male employees have expressed interest in serving on a 5 person committee to negotiate a new contract. A random drawing is held and no women are chosen. The women who had wished to serve on the negotiating team cry foul. How unusual is this sort of an event? S.ID.1, S.IC.2 Only 1 of the 100 simulated committees was exclusively male. S.ID.1, S.IC.2 20

Best Fest Presentation.notebook August 01, 2015 Another simulation Tom is standing at zero on a number line. He will toss a coin and move right if it lands on heads and left if it lands on tails. If he does this once, where might he stand? Estimate his chances of standing in each location. What if he tosses the coin twice? What if he tosses the coin four times? S.ID.1, S.IC.1 (Based on "Random Walk" items from illustrativemathematics.org) Another simulation http://www.personal.psu.edu/dpl14/java/probability/plinko/ 21