Probability and Data Management AP Book 8, Part 2: Unit 2

Transcription

1 Probability and Data Management AP Book 8, Part 2: Unit 2 AP Book PDM8-6 page ; The number of people doubled, so you can expect the number choosing Action to also double (15 2 = 30). To get frequency, divide each percent by 5 (0 ). Type % Comedy Horror 8 16 Action Other Mark Tally Freq % A //// 4 B //// //// / C /// 3 15 D // 2 3. a) Type Pop 7 Hip Hop 9 Rock 3 Other 1 i) ii) AP Book PDM8-7 page 39 Relative frequency; may not play songs want the correct proportion. 2. a) Yes No; A higher percentage at School A chose Action, but this doesn t necessarily mean more people. No; The statement is false since less than half prefer Action. Yes = 4% but, to be correct, the percents must add to a) Instead of looking at the size of the sections, Lina must look at the percent of A students at each school: School A: 26% School B: 30% The graphs should be drawn using circles that are the same size. AP Book PDM8-8 page Type Fraction % Mystery Fantasy Romance Other Other = = = = Mystery 2. a) walk 25% 90 bike % 72 bus 35% 126 car 15% 54 5% = 0% = , %; 126, 35%; 54, 15%; 18, 5% Teacher to check. 3. a) delivered 40% 144 occasionally 50% 180 never % 36 Daily Newspaper Habit never buy occasionally entertainment 45% 162 clothes 30% 8 snacks % 36 savings 15% 54 How Students Spend Money savings delivered to home entertainment apple % 72 blueberry 15% 54 cherry % 36 55% 198 Favourite Kind of Pie 4. a) 30, 30% 28, 28% 45, 45% 11, 44, 44% 4, 40, 40% f) 13, 65, 65% 5. a) , 63 7, a) Fraction Angle board card video = = = 1 12 Favourite Indoor Games apple cherry blueberry board C A H O T A B %; Yes, since the circle graphs include all the responses. Romance Fantasy snacks clothes video card Answer Keys for AP Book 8.2 V 9

2 Fraction Angle Company B: 0 f) Decreases hockey swimming running running 8 = = 1 Favourite Sport swimming AP Book PDM8-9 page % % 77. 7% 2. Answers may vary slightly a) A: %. B: % C: % PT FT A B C Company A; Circle graphs only show percents, not numbers. Although Company A only has % part-time staff (while B has 40%), it has times as many employees. 3. a) Company A: 40 hockey % # under over Number of Employees % # under over Employee Distribution i) A, bar ii) A, circle iii) A, both iv) B, both 4. a) = 58.3% = 30.6% = 27.8% = 26.7% 5. a) = % = % = % = % % 6. Answers may vary slightly a), B/G V F D P % Yes = 1% 0%; This is the result of rounding up to whole numbers. B/G V F D P # f) Yes AP Book PDM8- page 45 Circle: the dot in the top/right hand corner of the plot, at (14,170). Kevin and Melanie; Their dots are right beside each. NOTE: If they were actually one on top of the, it would only look like one dot! INVESTIGATION A. a) 3 Taller No Increase The plot shows a definite trend: it goes upward as it moves to the right. B. a) Not affected by age There is no pattern to the dots just randomly placed. 2. a) Decreases Is not affected 3. In a), it makes sense that the colder it gets outside, the more electricity you ll use (for heating and even for lights, since winter days are shorter). On the hand, in, it makes sense that the phone bill and outside temperature aren t related. 4. a) Increases Is not affected Increases Is not affected Decreases g) Increases h) Increases i) Decreases (assuming the numerator remains the sam 5. Selections will vary 6. a) Generally, that as a country s area increases, so does its population. see marks below 7. vs Height Gender vs Height Gender vs, V Answer Keys for AP Book 8.2

3 a) Agree; In the 2 nd plot, male heights are generally more than female heights. Agree; In the 1 st plot, there is an upward pattern. Disagree; The 3 rd plot shows that male ages are the same as female. 8. a) $ Housing Prices in Toronto (Tasfia) Price ($ 000) There is generally a price increase as the number of bedrooms increases. Housing Prices in Toronto (Ahme Price ($ 000) # of bedrooms two factors related to house price (e.g. # of bedrooms and subway distanc don t relate to one an. Ahmed should compare these factors directly (ideally with a larger data sampl to see if any relationship exists. AP Book PDM8-11 page 48 Scatter plot: Gas Usage in Sarah s Car Line graph: Gas Usage in Sarah s Car They are identical except for the joining line in the 2 nd graph. The scatter plot shows no obvious relationship: gas doesn t clearly increase or decrease in relation to speed. f) Between 30 and 45, and between 5 and 1 so the biggest change in gas consumption occurs between these points. g) The line graph; the line shows a distinct pattern one that isn t clear from the scatter plot. 2. a) Scatter plot: Line graph: There are 4 different (and correct) ways to join up the points in the graph. 3. a) Line graph: Sarah s height (cm) Sample explanation: I chose a line graph because the data is for a single person s foot size and height over time. I can see that Sarah s height increased as her foot grew so yes, there is a relationship. Scatter plot: Height (cm) Sarah s foot length (inches) Foot length (inches) Sample explanation: I chose a scatter plot because the data is a random sample of different people s foot size and height, all at the same point in time. In general, I see that height and foot size are related: as one increases, the one also tends to increase. distance from subway (km) There is generally a price decrease as the subway distance increases. f) In Q7, we saw that height relates to both age and gender, but that age and gender themselves had no relationship. This may be true here as well: that the Yes, it descends first, then remains quite constant before climbing sharply; it s shaped like a U. There are two different data points at both 30 km/h and 0 km/h. A scatter plot lets you easily represent these multiple points. AP Book PDM8-12 page 49 Answer Keys for AP Book 8.2 V 11

4 Interval Freq Histogram (continuous data) ii) No Make each interval 1 km instead of 2 km. BONUS A stem and leaf plot 6. a) Average Has too few intervals 3. Intervals may vary Times Tally 90 0 /// //// 4 Hours spent on homework each week Bar graph (discrete categories) //// / //// / //// / 6 Margaret s The new data is between intervals: > $899 but < $900. Answers may vary f) Sample: of Weekly Salaries Favourite ice cream 3. a) Histogram Bar Graph Both Both Histogram f) Both a) Marks Tally / / /// //// /// / //// 5 4. Intervals may vary Hours Tally 0 2 // //// 5 Number of employees of Weekly Salaries g) a) Bar graph (discrete categories) Number trying out Number of employees Weekly Salary ($) Position Histogram (continuous data) Weekly Salary ($) 4. Answers will vary Sample answers: Similarities Have labels, titles and a scale; Bars represent frequency of category; Bars are equal width. Differences In a histogram: Bars touch each ; Categories are numeric intervals, listed in order, and they re continuous and the same size. In a bar graph: Bars have space between them; Categories are discrete; Order of categories doesn t matter. 5. a) i) 70 ii) 40 + = 50 iii) 30 i) No Number of people See grey box on page 49: it s on the interval s border. AP Book PDM8-13 page a) Doesn t cover the entire range of data Contains intervals of different sizes Has too many intervals 4 6 //// // //// 4 8 // 2 Weekly Time Spent on Homework (Grade 8 students) 5. a) Hours (per week) Histogram Relative Histogram Answers will vary V 12 Answer Keys for AP Book 8.2

5 Spending by Charity A Graph B Circle graph Time % Angle Medical Supplies Fundraising Election Results Paul Melanie Katie Money Spent (in millions) Time to School (in minutes) i) Less than minutes (either circle or histogram) ii) Decrease (histogram) iii) Less than half (either circle or histogram) iv) 32% (histogram) AP Book PDM8-14 page Spending by Two Charities Spending Category 0 Charity A % Angle Fundraising 30 8 Shipping 72 Admin Supplies Administration Charity B % Angle Fundraising Shipping Admin 36 Supplies Medical Supplies Spending by Charity B Administration Shipping Fundraising Shipping i) A, double bar ii) A, double bar iii) 35%, circle iv) 40%, circle $35 $40 f) Charity B; a larger percentage will go to supplies g) Circle; care less about the amount of $ spent and more about the allocation of funds 2. Graph A a) A B B No; the provinces are discrete categories 3. 5: Shows how data is divided 6: Visually displays the freq of results for continuous data. 1: Compares two sets of data 3: Visually displays the freq of results. f) 4: Shows whether one type of data 4. a) 1: Circle graph 4: Histogram 6: Line graph 5: Double bar graph 2: Bar graph f) 3: Scatter plot 5. a) Bar graph Double bar graph Scatter plot Circle graph Line graph f) Histogram 6. Scales may vary a) Histogram of Tennis Club Members Mark Weekly allowance ($) # of occurrences Rita John Double bar graph Jessica s Marks Test Scatter plot Weekly Allowance by Bar graph Number of Pets Students Have Number of pets f) Line graph Annual of Friday 13 th Year Answer Keys for AP Book 8.2 V 13