Number of members Math 310 Fall 2007Test #1 Statistics & Probability ANSWERS SHOW WORK as if making a solutions guide for students. Use extra paper if necessary. Don' t forget#1-3 The ages, in years, of ten members of the IHHAA are given below. labels, scales,75 96 96 93 84 54 51 75 69 24 & legends!() 1. Classify the data in a Ages of ten members of the IHHAA* st em-and-leaf diagram. 2 4 so there are at least 3 five classes. 4 5 1 4 Legend 6 9 5 1 4 7 5 5 8 4 represents ages 51 & 54 years 9 3 6 6 of tw o members of IHHAA* International Habitat for Humanity Alumni Assn.Ages of ten members of the IHHAA() 2. Draw a hist ogram using classes which . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . correspond to those 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . in problem (1). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20-29 30-39 40-49 50-59 60-69 70-79 80-89 90-99Years of age() 3. Draw a box plot* for this data. * Not a line plotAges, in years, of ten members of the IHHAA * Not a . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . bar chart. ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ! . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 54 75 93 96 WORK û 24 51 54 69 75 ^ 75 84 93 96 96 Min 1Q 2Q3Q Max IQR = 93 – 54 = 39 Test value for outlier = 1.5 (39) = 68.5 ... No outliers.() 4. Choose (circle the letter of) the BEST completion of each statement. For data A, show n at right, it appears: . Athe median is greater than the mean.The data is skew ed left (see the “ Tail” ).If data were symmetric (see the red line), then mean would = median. When skew ed left , the very low values in the tail “ pull” the mean down,but do not have the same effect on the median. “ Tail” ÷ So the mean is below the median, thus the answ er above.. !100 !75 -50 0 50 ² In B, many data In D, the data are moreOf these three data distributions, are clustered close “spread out” . AverageB & C & D, the one w ith the B to the mean. C distance to mean greatest standard deviation is: D is greater here. D The average distance to the meanis greatest for distribution D.This w ill also be true for the s.d. !100 !50 0 50 100 !100 !50 0 50 100 !100 !50 0 50 100the s.d. is greatest for distribution D.() 5. Showing ALL your work, construct a pie chart illustrating the distribution of school expenditures. In the ALUFSD Unified School District, the follow ing yearly expenditures are made for each student:Teaching staff salary & benefits: $2700 ALUFSD Unified School DistrictSchool plant maintenance: $1800 yearly expenditures per studentInsurance & Administration: $3600))))))Total expenditure per student: $8100Teaching salary etc. deserves 2700/8100, or Teaching 1/3 of the circle. Insurance Staf f1/3 of 360E = 120E sector & Salary & Administration BenefitsSchool plant and maintenance should have $3600 @ $27001800/8100 = 2/9 ...2/9 of 360E = 80E sector. (44%) (33%)Ins. & admin. get 3600/8100 = 4/9 of the pie, Facilit iesor a sector w ith 4/9 of 360E = 160E cent ral angle. Maintenance $1800Note: explanation shown above ^| constitutes “ showing your work”. (22%)Not ice this does not mean scribbling computations all over the page,but making clear how the w ork is being done.() 6. Showing your work, for the quiz scores in the frequency table at right: quiz score frequency a. calculate the mean. b. calculate the standard deviation. 3 1 7 1E(x)6a. Mean = )))) 10 3 n 3 @ 10 + 7 + 3 40= ))))))))))))))) ) = ))) = 8 5 5NOTE: A mean low er t han 3 or higher t han 10 is clearly impossible! (Why?)E(x – mean) 26b. Variance = ))))))))))n 3 @ (10– 8) + (7– 8) + (3– 8) 3@4 + 1 + 25 38222= )))))))))))))))))))))))))))) = ))))))))))) = )) = 7.6 5 5 5 Std Dev = q% %7%. %6% % NOTE: Std dev should be more than 0 and less than 3.5. It is!() 7. The 25 students in Miss Horne' s 4th-grade averaged 60 on the state reading test; the remaining 15 4th-graders, in Mr. King' s class, averaged 80. What is the mean for all the fourth graders?Total (of all tests) points mean = ))))))))))))))))))))))# of tests 25@ 60 + 15@80 ²Total points from Horne’s class, plus total from King’s class. = )))))))))))))))25 + 15 ² # of tests from Horne’s plus # from King’s class. Note Horne’s 25 students have …