North Point - Advance Placement Statistics This assignment is due during the first week of class. It is considered an exam grade, which that category is worth approximately 60% of your total grade. All work must be shown and graphs need to be drawn accurately and neatly on separate paper. Any work done using technology must be documented. This assignment is designed to reinforce concepts already learned and to practice the preliminary information of the course. Each topic contains a brief description, directions, an example, and problems for you to complete. Starred topics are of major importance. Further directions (if needed) can be found online, or any questions can be directed to tcerutti@ccboe.com. Topic: Segmented Bar Graphs (Stacked Bar Graph) -similar to regular bar graphs except the bars are made of different subdivisions (segments) -length of each segment indicates the proportion (or percentage) of observations in a 2 nd variable -the focus is on the make-up (distribution) and values within the bar rather than the whole Example: Is there a home-team advantage? Below is a random collection of data from three sports over a span of the last 5 years. Create a segmented bar graph that shows the distribution of wins based on each sport. Home Team Wins Visiting Team Wins Total Baseball 632 608 1240 Hockey 259 165 424 Basketball 420 98 518 Total 1311 871 2182 Steps: 1. Identify the two variables (underlined above) 2. Directions want a distribution of wins based on sport, so sport is the x-axis and the subdivisions are: (1) Home-wins and (2) Visiting-wins 3. Calculated each subdivision s proportion (%) 4. Each sport s subdivisions should add to 100% 5. Graph the percents, stacking them! Baseball: Basketball: V-Wins = 608/1240 =.490 V-Wins =.189 H-Wins = 632/1240 =.510 H-Wins =.811 Hockey: V-Wins = 165/424 =.389 H-Wins = 259/424 =.611 1. Felipe surveyed students at his school about BYOD. He found that 280 out of 320 students who own a smartphone would use it at school; 140 out of 220 students who own a tablet would use it at school; and 60 out of 140 who own a laptop would use it at school. Construct a segmented bar graph that shows the willingness to use technology based on the type. 2. The two-way table shows the places that males and females volunteered in the past month. Make a segmented bar graph to see if there are volunteer differences among people, based on gender. 18 7 25 20
Topic: Stemplots -used to visually organize and order a set of data; describes the shape or pattern of data Shape: symmetric or slanted Odd: gaps, clusters, etc. Center: Mean or Median Spread: Range -requires a stem, leaves, and a key -order the data, then create a stem by grouping by 10s, 100s, etc., write the remaining parts outwards as the leaves, finally make a key Example: Traffic violations are serious and cause numerous accidents. One insurance agency wants to know how much the different municipalities fine drivers for these violations. Below are the fines assessed to drivers who failed to stop at a stop sign. 128 122 125 134 137 125 165 118 130 126 128 119 120 121 157 166 151 153 117 125 133 121 122 120 118 127 In order: 117 118 118 119 120 120 121 121 122 122 125 125 125 126 127 128 128 130 133 134 137 151 153 157 165 166 S-slanted towards higher values O-gap at the $140s, might have outliers at 165 and 166 C-median is $125.5 S-the range is from $117 to $166 11 8 = 118 3. The weight of a baby grand piano can weigh up to 800lbs. Below are the weights of 18 baby grand pianos. Create a stemplot of this data. Describe the data (look above S.O.C.S. ) 654 741 686 711 697 740 728 700 671 687 711 660 656 711 728 729 712 662 4. Studies have shown the benefit of taking an AP course in high school on post-secondary achievement, regardless of performance. However, none of these studies looked at AP s effect on happiness during high school. Students gave a rating (from 1 5) about their high school experience, where 1 is an ultimately negative feeling and 5 represents a pristine impression of high school. In each school, an average rating for AP and non-ap students were calculated and a random sampling of both are shown below. AP Student Non-AP Student 3.6 4.6 4.1 2.7 5.0 4.2 2.6 2.9 5.0 4.1 3.2 4.2 4.0 2.4 4.6 2.0 3.1 3.7 1.6 4.3 4.3 3.5 3.3 3.4 3.9 3.5 1.1 3.3 3.6 2.4 3.3 2.1 2.5 Construct a back-to-back stemplot (using the same stem see example ) for the two types of students. Describe and compare the two types and interpret in context what this means about AP s effect on happiness during high school.
Topic: **Boxplots** -commonly used to provide a brief description of the center and spread of data -divides the data into sections called quartiles -order the data, find the (1) median, find the (2) first quartile and (3) third quartile (the medians of the two halves you created), find the (4) lowest value (min) and (5) highest value (max). Next, graph these points on a number line (as shown in the picture). -if you find two middle terms, calculate the average between them. Example: The following are the shoe sizes of 15 students in a classroom. Create a boxplot. 8.0 8.5 6.0 9.0 9.0 8.5 10.0 7.0 5.0 6.0 8.5 7.0 7.5 12.5 6.5 5 6 6 6.5 7 7 7.5 8 8.5 8.5 8.5 9 9 10 12.5 Median = 8 5 6 6 6.5 7 7 7.5 8 8.5 8.5 8.5 9 9 10 12.5 First Quartile = 6.5 Third Quartile = 9 Scaling: Count by the same amount on the number line Shoe Size of Students in a Classroom 5. Below are 19 scores from a previous exam. List the 5 values, and create an accurate boxplot. 65 77 85 81 91 96 78 84 77 54 65 71 74 55 88 64 96 76 86 6. The number of memes posted by several young adults, about school over the course of a year, is shown below. List the 5 values, and create an accurate boxplot. 14 19 25 17 21 32 44 27 39 26 29 33 36 36 16 41 37 51
Topic: **Histograms** -commonly used to describe the shape of a distribution, especially to check normality -separates the data into equivalent intervals and displays a frequency for each interval. -histograms require at least 5 intervals (your choice on the common width see box below) -order the data, create intervals that separate the data, count how many observed values fall within each interval, then graph the intervals along the x-axis and the frequencies along the y-axis Example: A new golf course petitioned the PGA for inclusion in next year s competitions. Before the PGA will accept the golf course, they asked 27 professional golfers to test the course and report their total strokes. If the golfers scores were too far below par (72) they would have to deny the petition. 68 70 78 66 69 71 71 70 74 81 77 68 70 70 69 71 72 73 75 77 67 65 67 82 70 65 68 Interval Width: Range is 82 65 = 17 5 Intervals 17/5 3.4 6 Intervals 17/6 2.8 I chose a width of 3 points Intervals Frequency 65 67 (3 points) 5 68 70 10 71 73 5 74 76 2 77 79 3 80 83 2 7. The number of days between UFO sightings filed with the Roswell police department were tracked and listed below. Create a histogram of the number of sightings. A suggested interval width is 5. 15 19 24 25 36 38 41 36 41 43 26 41 31 26 37 19 31 36 41 44 18 23 34 29 40 29 35 38 42 44 8. What is the fastest you have ever driven a car? mph was a survey taken in a large statistics class at a large university. The data below shows the anonymous responses provided by 36 females. Construct a histogram. A suggested interval width would be 10 mph. 96 95 96 73 91 67 94 78 81 87 90 75 88 90 102 86 100 75 69 84 70 91 110 105 95 75 74 90 72 83 85 71 100 112 87 68
Topic: Relative Cumulative Frequency Graphs (O-gives) -used to describe the relative standing of an individual compared to the population -converts the frequencies into percentages (showing percentiles) -order the data, create intervals that section the data (at least 5), count how many observed values fall within the interval, calculate the relative frequencies, then the cumulative relative frequencies, finally graph the intervals along the x-axis and the cumulative relative frequencies along the y-axis Example: The expected age of teachers is getting younger. Using the following data, construct a relative cumulative frequency graph. Would a teacher at the age of 27 be unusually young? Summary data from 54 teachers is shown in the first two columns. Teacher s Age Frequency Relative Frequency Cumulative Frequency Relative Cumulative Frequency (no overlap, by 5 s) #s within the int. Freq / Total Add up freqs. C.F. / Total 20-24 9 9/54 =.1667 9 9/54 =.1667 25-29 12 12/54 =.2222 9+12 = 21 21/54 =.3889 30-34 13 13/54 =.2407 21+13 = 34 34/54 =.6296 35-39 7 7/54 =.1296 34+7 = 41.7592 40-44 4 4/54 =.0741 41+4 = 45.8333 45-49 5 5/54 =.0926 45+5 = 50.9259 50-54 3 3/54 =.0556 50+3 = 53.9815 55-59 1 1/54 =.0185 53+1 = 54 1.00 9. The following are scores from an arithmetic test administered to 20 eighth-graders. Create a relative cumulative frequency graph from this data. 8 24 24 21 28 21 2 11 23 32 23 13 25 21 14 8 17 23 13 11
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Please attach this scoring rubric to the front of you summer assignment. Name: Block: Date submitted: Question Score (out of) Teacher Notes (from me to you): 1 / 3 points Looking for calculations, graph, labels/legend 2 / 3 points Looking for calculations, graph, labels/legend 3 4 5 6 / 1 point / 3 points / 1 point / 3 points SOCS: SOCS: #s: #s: 7 / 4 points Table of Consistent Intervals and Frequencies, Graph 8 / 4 points Table of Consistent Intervals and Frequencies, Graph 9 / 4 points Intervals, Frequencies, Relative Frequencies, Graph