Number of countries Math 3 10 Fall 2006 Test # 1 St atistics & Probability ANSWERS SHOW WORK as if making a solutions guide for student s. Use extra paper if necessary. Don' t f orget#1-3 The scores of ten countries on t he PISA* test are given below . labels, scales,5.5 5.2 5.2 5.1 5.8 4.8 4.7 5.5 5.3 3.8 & legends!(5) 1. Classify the data in a Scores of ten count ries on t he PISA stem-and-leaf diagram. 3 8 so there are at least 4 five classes. 4 7 8 5 1 2 2 3 Legend 5 5 8 4 7 8 represents scores of 47 & 48 for some count riesScores of ten count ries on t he PISA(6) 2. Draw a hist ogram . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . using classes which . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . correspond t o those 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . in problem (1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 0. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 - 3.9 4.0 - 4.4 4.5 - 4.9 5.0 - 5.4 5.5 - 5.9Score on PISA test(12) 3. Draw a box plot for t his data.Scores of ten count ries on t he PISA A . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . box plot ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! . . is not . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . a 3.8 4.8 5.2 5.5 5.8 line plot ! WORK û 3.8 4.7 4.8 5.1 5.2 5.2 5.3 5.5 5.5 5.8Min Q1 Q2Q3MaxIQR = 5.5 – 4.8 = .7Test value for outlier = 1.5 (.7) = 1.05 No outliers....(6) 4. For the data below, choose (circle the letter of) the best completion of these two statements: It appears:the mean and median are t he same. The data is skewed right (see “Tail” ).the median is greater than the mean.the mean is greater than the median. The higher values in the tail “pull” thethere is no median, but there is a mean. mean up, w hilethere is insufficient inf ormation t o draw any conclusion median is about the relativ e positions of t he mean and median. unaffected.The standard deviation could be: “Tail”0 ² Data show n is not all one value! about 10 ² Most of the data is further than 10 from the mean. !100 !50 0 50 100about 50 ² Most of the dat a falls w it hin 10 0 unit s of the mean.about 200 ² All the data is closer to t he mean than 200.There is a st andard deviat ion, but it could not be near any of the values above.There is insuf ficient inf ormation to draw any conclusion about the standard deviation.(9) 5. Showing ALL your work, construct a pie chart illustrating the distribution of school funds / student. In the UFSD Unified School District, the follow ing yearly expenditures are made for each student:Teaching staff salary & benefits: $2100School plant maintenance: $1400 UFSD Unified School DistrictInsurance & Administration: $2800 yearly expenditures per student))))))Total expenditure per student: $6300Teaching salary etc. merits 2100/63 00, or Teaching 1/ 3 of the circl e. Insurance Staff1/3 of 360° or 120° sector & Salary & Administration BenefitsSchool plant and maint enance should hav e $2800 @ $21001400/630 0 = 2/9 ...2/9 of 36 0° = 80° sector (44%) (33%)Ins. & admin. get 28 00 /6 30 0 = 4/ 9 of the pie, Facilitiesor a sector w it h 4/9 of 36 0° = 16 0° cent ral angle. Maintenance $1400Note: the above constitutes “showing your work” . (22%)Not ice t his does not mean scribbling comput ations all over the page,but making clear how the w ork is being done.(12) 6. Showing your w ork, for the quiz scores in the frequency table at right: quiz score frequency a. calculat e the mean. b. calculat e the standard deviat ion. 6 4 8 1E(x)6a. Mean = )))) 10 1 n 4 @ 6 + 8 + 10 42= )))))))))))))))) = ))) = 7 6 6NOTE: A mean low er t han 6 or higher t han 10 is cl earl y impossi ble! (Why ?)E (x – mean)2 6b. Variance = ))))))))))n 4 @ (6– 7)2 + (8–7)2 + (10– 7)24@1 + 1 + 9 14= )))))))))))))))))))))))))))) = ))))))))))) = )) 6 6 6 Std Dev = q %7% /%3% % %NOTE: Std dev should be more t han 0 and less than 2. It is!(5) 7. The 25 students in M iss Horne’s 4th-graders averaged 70 on the state reading test; t …