(a) frequency (b) mode (c) histogram (d) standard deviation (e) All the above measure

Transcription

1 MT143 Introductory Statitic I Exercie on Exam 1 Topic Exam 1 will ocu on chapter 2 rom the textbook. Exam will be cloed book but you can have one page o note. There i no guarantee that thee exercie will provide good approximation to the actual tet quetion. Thi i merely an extra et o exercie. Exercie 1. Which o the ollowing tatitic i not a meaure o central tendency? (a) mean (b) tandard deviation (c) Median (d) Mode (e) All the above meaure central tendency 2. Which o the ollowing i a meaure o diperion? (a) requency (b) mode (c) hitogram (d) tandard deviation (e) All the above meaure diperion 3. Many proeional chool require applicant to take a tandardized tet. Suppoe that 1000 tudent write the tet, and you ind that your mark o 63 (out o 100) wa the 73rd percentile. Thi mean : (a) about 73% o the people got 63 or better. (b) about 270 people got 73 or better. (c) about 270 people got 63 or better. (d) about 27% o the people got 73 or wore. (e) about 730 people got 73 or better. 4. A ample o 224 core produced the ollowing tatitic. Mean=100 Q 1 =70 median=95 Q 3 =120 mode=75 tandard deviation=30 Which tatement i correct? (a) Hal o the core are le than 100. (b) The mot common core i 95. (c) The variance i (d) One quarter o the core are greater than 100. (e) None o the above. 5. The median o 5, 9, 20, 8, 6, and 2 i: (a) 14 (b) 20 (c) 7 (d) 6 (e) 8 6. The median o 1,5,1,6,1,6, and 8 i: (a) 1 (b) 4 (c) 5 (d) 6 (e) 8 7. The height o the adult in one town have a mean o 67.2 inche and a tandard deviation o 3.5 inche. What can you conclude rom Chebyhev theorem about the percentage o adult in the town whoe height are between 60.2 and 74.2 inche? (a) The percentage i at mot 95% (b) The percentage i at mot 75% (c) The percentage i at leat 75% (d) The percentage i at leat 95% 1

2 8. Which o the ollowing tatement about the median i not true? (a) It i equal to Q2. (b) It i a meaure o central tendency. (c) It i equal to the mode in ymmetrical ditribution. (d) It i more aected by extreme value than the mean. (e) None o the above. 9. A company give yearly perormance rating to each o it employee. Thee rating are E or exemplary perormance, A or acceptable perormance and I or perormance needing improvement. The 24 employee in the receiving department were given the ollowing rating: A A A E I E E A E A A I E A I A A E E A A I E E What type o graphical diplay hould you ue or thi data? (a) a hitogram. (b) a tem and lea plot. (c) a bar graph. (d) a boxplot. 10. Suppoe that you are about to purchae a car and have narrowed your choice to two model-model A and Model B. All thing are about equal, uch a price, option, even the average annual maintenance cot. You ind an owner urvey in an auto magazine that indicate that the tandard deviation o maintenance cot i maller or Model B. Baed on thi inormation, which o the ollowing tatement i mot appropriate? (a) Model A with the larger tandard deviation i preerable, becaue the larger value implie a maller amount o variation in the data. (b) Model B with the maller tandard deviation i preerable, becaue the maller value implie that the mean i a more reliable repreentation o maintenance cot. (c) They are equally acceptable, becaue tandard deviation are not ueul or comparion o data et. 11. Many tudent are curiou about the 1.5 IQR Rule, i.e. why do we ue Q IQR (or Q IQR) a the value or deciding i a data value i claiied a an outlier? Paul Velleman, a tatitician at Cornell Univerity, wa a tudent o John Tukey, who invented the boxplot and the 1.5 IQR Rule. When he aked Tukey, Why 1.5?, Tukey anwered, Becaue 1 i too mall and 2 i too large. Quetion: For a data et, Q 1 = 29 and Q 3 = 55. Which o the ollowing are outlier? { 23, 17, 0, 27, 42, 78, 88, 90}. 12. Conider the ollowing requency ditribution: x (a) Determine the mean and tandard deviation or the variable x. (b) Approximately what percentage o uch data will be included between µ σ and µ + σ? 13. A nationally adminitered tet ha a mean o 500 and a tandard deviation o 100. I your tandard core on thi tet wa z = 1.92, what wa your tet core? 14. A nationally adminitered tet ha a mean o 500 and a tandard deviation o 100. I your tandard core on thi tet wa z = 1.8, what wa your tet core? 2

3 15. The ollowing data repreent the number o people aged covered by health inurance in 1998: Age Number () (in million) = (a) What proportion o people aged i or more than 55 year old. (b) Repreent the grouped data with a hitogram. On the ame graph contruct a requency curve. (c) Decribe the hape o the ditribution (ymmetric, kewed right, or kewed let), a illutrated by the hitogram. 16. Conider the inormation given in the table below, concerning the number o broken bicuit ound in ome packet o chocolate inger. (a) What i the median o the ditribution? (b) What i the mode o the ditribution? 17. Conider the ollowing population (a) Find the mean µ and the tandard deviation σ. Number o broken bicuit (x) Frequency () (b) Exactly what proportion o obervation are within 1 tandard deviation o the mean? (c) Exactly what proportion o obervation are within 3 tandard deviation o the mean? (d) What doe Chebychev rule predict or the proportion o obervation that are within 3 tandard deviation o the mean? Doe your reult in (c) agree with that prediction? 18. Fiteen randomly elected college tudent were aked to tate the number o hour they lept lat night. The reulting data are (a) Given that the tandard deviation or thi ample i 1.75, approximately what percentage o uch data will be included between x 2 and x + 2? 19. A requency ditribution o 101 item i the ollowing: Clae Frequency() = 101 (a) Find the mean µ and the tandard deviation σ. (b) What proportion o data i le than (c) Repreent the grouped data with a hitogram. On the ame graph contruct a requency curve. 3

4 20. Which x-value ha the higher value relative to the et o data rom which it come? (a) x = 85, where mean = 72 and tandard deviation = 8. (b) x = 93, where mean = 87 and tandard deviation = A data et ha ize n = 224 and ive number ummary: 20, 80, 100, 150, 155. (a) How many obervation have value le than 100. (b) How many obervation have value more than 80. (c) According to the 1.5 IQR or outlier, are the maximum 155 and the minimum 20 outlier? 22. Draw a boxplot or the et o data whoe ive number ummary i : 42, 62, 72, 75, 97. Doe the boxplot how any outlier? 23. According to the tatitic o the Quick and Eay Data Company, amily income in Martian County have the ollowing percentile rank: P 25 = $12, 000 P 50 = $20, 400 P 75 = $30, 600 P 90 = $43, 500 State approximately the percent o the amilie which earn i. Le than $12, 000 ii. More than $43, In a tudy o wate dipoal in Noewer County it wa dicovered that the mean amount o garbage wa 30 pound per day per amily and the median wa 35 pound per day per amily. Which one o the ollowing i true? i. Exactly hal the amilie produced 30 pound or more o garbage. ii. More than hal the amilie produced 30 pound or more o garbage. iii. Le than hal produced 30 pound or more o garbage. 25. The value o z i actually a meaure o how ar any point i away rom the mean. i. True ii. Fale 4

5 ANSWER KEY Exercie on Exam 1 Topic 1. (b) 2. (d) 3. (c) 4. (e) 5. (c) 6. (c) 7. (c) 8. (d) 9. (c) 10. (b) 11. IQR = Q 3 Q 1 = = 26, o lower ence= Q IQR = = 10, and upper ence= Q IQR = = 94. Hence, the ollowing are outlier: 23, (a) The mean i µ = x x (x µ) 2 (x µ) = 56 x = 52 (x µ) 2 = The tandard deviation i σ = x = (x µ)2 = =.5663 = (b) Firt, µ σ = =.1775 and µ + σ = Thereore, = 53.57% o the data i between µ σ and µ + σ 13. Subtitute in z = x x 14. Subtitute in z = x x to obtain 1.92 = x , rom which x = 692. to obtain 1.8 = x , rom which x = (a) %. (b) See Chapter 2 in the lecture note or the textbook. (c) See Chapter 2 in the lecture note or the textbook. 16. (a) Median = 4, (b) Mode = (a) µ = and σ = To anwer the remaining item, contruct a cale a we did in the cla, or ee item (b) o the next exercie. 18. (a) Firt, the Mean = 6.9. Now, x 2 = 6.9 2(1.75) = 3.4 and x + 2 = (1.75) = Thereore, = 93.33% o the data i between x 2 and x Cla Frequency () Cla mark x x (x µ) 2 (x µ) = 101 x = (x µ) 2 = (a) The mean i µ = The tandard deviation i σ = x = (x µ) 2 = =

6 20. (b) The proportion o data which i le than 8.35 i = 76.23% (c) See your cla note or the textbook. (a) Subtitute in z = x x (b) Subtitute in z = x x to obtain z = = to obtain z = = 1.2. Thereore, x = 85 ha the higher value relative to the et o data rom which it come. 21. (a) = 112 obervation have value le than the median 100. (b) = 168 obervation have value le than the irt quartile 80. (c) Firt. IQR = Q 3 Q 1 = = 70, o lower ence= Q IQR = = 25, and upper ence= Q IQR = = 255. Hence, the the minimum 20 and the maximum 97 are not outlier. 22. See your cla note or the textbook. 23. i. 25% o the amilie earn le than P 25 = $12, 000. ii. 10% o the amilie earn more than P 90 = $43, i. Fale ii. True iii. Fale 25. True 6