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Towson - ECON 205 - Study Guide - Final

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I study Guide Exam Sections: I. Sampling « Population > graphs Is Frequency Tables + Graphing TII, Standard Deviation II. Empirical Rule I Chebyshev I. Sampling and Population Mainly word problems with proportions. Sample Problem A bin is filled with balls, but we don't know how many there are. We do Don't forget about the age old question of ∙ What is a mini-cog?

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know that there are 40 orange balls in the bin and the rest are white, Anna candomly selects 20 balls of which 6 were orange, Based on this sample how many balls are in the bin? 2 - 76: 100=6001 -> 203600 = 20/30% 40.100=4,000 --> 30.14,000 --> 133,33 There are 133 balls in the bin) 1. Frequency Tables and bacaphing that Category (probability) relative free % com, f(a) 290, 310, 398, 395 419, 425, 450, 450, 475, 510 Categories, 250-300 301-350 351-400 40-450 451 - 500 501-550/ 30% how many in that cat o previous categories 10% 10 bumbay 201 351 Hol 15 V in calceories to show frequency Categories I Standard Deviation MAD Xi Xi-mean, (Xi - meand 239 mean = median 240 225 mean> median 392 25 100 496 Standard deviation (51) - Elxi-mean? mean = 405 median = 405 range - 398-430 mean average deviation (MAD) = 6 lx; -mean! meant - to be identical The wider the graph, the higher the height indicates the mode. The higher the graph, the more mode, The forther along the x-axis, the greater the mean and median the soi 1. Empirical hule General Equations For finding % Z = CutPorn mean ER% For finding cutpants- use % to find Z (1,2,3), then use mean I ZSD ER EISD ~ 68% # 250 7 950% +350 a 99,7% Between above, be low- add as if one negative & one positive z - Subtract # if both positive or both negative Finding Percentage Stepsi Cutpoint mean 1. Find the 2 score(s) using Z=" 9D 2. Use a scares to find percentage (s), 3. Divide percentage (s) by 2. 4, Either add numbers, subtract numbers, add 50 to number, or subtract 50 from nomides, Problems 1. Find the percentage above 70. Mean of 100, Meclion of 100, SD of 10. Z= 70-100 = = -3 99,7% 259917 49.85 70 100 50,00 +49.85 2. Find the percentage between 120 + 90. Meen of 100; Medion of 100, D of 10 Z= 120-100 = 20 = 2 95 2095 47,5 A z 90-100 = 1 4 68 +268 34 90 100 120 one neg. Z and one pos. Z 47,5 means you add the numbers, 34,0 I 100 70 90 15.85% 3. Find the percentage between 70 90. Mean of 100; Median of 100 ; SD of 10. 7= 70-100 3 3 99,7 2,997 49,85 49.85 z = 90-1000 H4 68 2168 34 34.00 both neg, need to subtract numbers 4. Find the percentage below 90. Mean of 100; Medicon of 100; SD of 10 Z = 480 = -0 = -1 → 68 2568 → 34 _50 - 34. 3450 16% 5. Find the percentage below 120. Mean of 100, Medion of 100; SD of 10 - 120-100 - 200 = 2 992595 → 47,5 50.0 90-100 47.5 97,5% 50 44,5 Finding Cutpoints Steps: 1 Is the given percentage 68, 95, 99.7, 34, 47,5, or 49,85 ? A. If no, subtract the given percentage by 50 to find the Z. B. If yes, identify if z is I1, #2, or 23 2. Input z score into mean & ZSD Problems 1. What is the cutpoint above which Mean & Median of 36 SD of 7 16% of the distribution falls? 36 À T O 50-16 = 34 Chalf of 68) mean + 1 SD mean – ISD In 68 36 +1(7) - 43 36 - {(7) = 29 29 would be too & lows for 16% to * be above it 2. 49.5% of the distribution falls between the mean and what 116. Bolo cut pointes)? Meano median of 36; SD of 7 49.5970 49,5% is half of 99.7 mean + 350 mean - 350 99.7% ~ +3 36 + (7)=57 36-3(7) = 15 X 36 X 57,15 3. What is the ctpoint below which 84% Mean & Median of 36 SD of 7 of the distribution falls? 84-50 = 34. mean + 1 SD 34= 1/2 of 68 / 36 + 1(7) = 43 6851SD mean - 151) 36-167) = 29 *29 would be too low of a number for 84% to be below it * 4. Find the interval containing 95% of the distribution Mean & Medion of 36, 5D of 7 959% 95% +25D mean + 25D mean - 250 36 +267) = 50 36-267) = 22 V. Chelyshev General Equations • Understanding Z=k To-1-x2 cutpoints = intervals When it says X deviations beturen, above or below, Kok Finding custponts) intervals when given el Steps 1. Plug in the percentage (in decimal form!) into % = 1 - 1 / 2 2. Find using above formula 3. Plug k into mean & KSD Pcoblems 1. Find the cutpoints for 91.84%. Mean is 51.54, Median is 37; SD is 7.51 7.9184 =12 > mean I KSD 46.9184K? = K2- 51.54 +3.5(7,51) = 77,83 77.83) 25.25 1.9184 KP-1K2=1 51.54 -3.517.51) = 25.25 ,0816 K2 = 1 k=video &k= 3,5 2. Find the interval containing 62% of distribution, Mean & median of 100 SD of 10. mean IKSD 100 + 1.622(10) = 116,22 100- 1.622(10) = 83,78 116.22, 83.787 6.62 = 1-722 [.62 =12 5.62Ko=1k-1 (.62k? 142 = -1 y -,38k? = -1 * 100 * GK=11622 Finding Cutpoint Above & Below Steps 1. Subtract or add 50 to given percentage based 2. Multiply new number by 2. Then, plug percentage into 3. Plug k into mean I KSD on the problem. = 1- Ez Problem 1. What cutpoint is required below which 17,5% - falls? Mean of 120, Medion of 130; SD of 15. of the distribution X 130 50-17.3= 32.79% 1321702= 65,40% 22 2654 = 1-2] 4. 654K2-162 1 4 - 346 k 2 = -1 (K=1.346 k = 12.890 "K= 1,700 Finding Peccentage When briven Cutpants > mean = KSD 120+ 1,7(15) -145.5 too high 120-117(15) = 94.5 94.5 Cutpoint mean Steps 1. Find klz by 2. Plug klz into = SD plugging cutpoints into Z % = 1-4 22 to find %. Problema 1. What percentage of the distribution falls between 400 and 600? Mean of 500; Medion of 500; SD of 40 600- 500 400 500 600 2.5 / 7%=1-7162 -2.52 and 218h are 60%=1-, 16 the same 9002 해 Standard Deviations Pemideri # of Standard deviations = k/z Steps: 1 Plug nunber of standard deviations into % = 1 * Make sure you do it in decirnal form * 2 distribution fall within 118 standard deviations Problem 1, What % of the %=1-722 of the mean? 169.14% = 1-3,24 - 1-3086 % =,6914 Prons Research Cycle - Statistics driven by Questions - Simulation (classroom research) - Descriptive stats f(x) table> Graphs fall mean, medion, mode Cats Given % find cutpoint (s) if normal ER mear ZSD if not ER → Chebyshev %= tz meant KSD Given cut pointesfind % if normal ER Z= Cutpont - mean? if not ER → Chebyshev cats a e Shapes of Distributions * - mean vs. median * -pearson coefficient tight, normal, left sken - Standard deviation dispersion - MAD Above - Applications of SD above below normal Eh Below Subtract ADD Subtrach ADD between Chebygher Subtract Subtract Between SD & MAD have to be relatively close to each other Quaciles Median = Q2 388 389 389,5 Qi 390 405 To find Q, & Qz, find median of upper half of scores & lower half of Scores 407.5 Q2 4120.5 QB Q = 25% Q2 = 50% Qz = 750% 415 426 430 Outliers UL> Q2 + [1.50 (03-01)7 420,5+ [1.50(470,5- 399,5)] 420,5 + 46.5 467 any score above 467 is an outler LL<Q, -[1.90(Qz-Q)] 399.5-2.501420,5-399.5] 389,5-46.5 [343 any score less than 343 is an outlier * Butlers Q2 = 36 Find cutpoints for outliers, Exande 1 Q = 24 Q2 = 30 UL 7 Q3 + [1.50 (Q3-Q,2 36 + 11.50 (36-28) ] 36 + 12 th < Q, -[1.501Q3-Q,)] 28 - 12 16 Percentiles P16 = 16% fall below cutpoint mean 65 SDIZ 16010 mean-15D ,547 chart (inside out) - 65-1(12) Z= cutpoint - mean ± 1,00 X-65 lyst -1.00 (12) +65 =_ nego because Cutipart=-2 -12465-63 Pqh = 84% falls below cotpoint mean 65 SD 12 84666 Baylo Z= cutpost mean 84 71.00 = * 450) 10002) +65 = 7 134 12 +65 = 177 X-65 Cufpoint-mean SD 12 Deciles split distribution into 10 parts Dz Cotpoint below which 20% falls 300 20% chart for 30% Cinside out) z= cutpoint - mean ~,94 = x-64 -,84 (12) +65=7 X=54,92 Can't use chart to I find outer ends of I When given % to find outpant, go inside-out on chart go outsid-in on chart When given cutpoint to find to Class Bank Ks. Peccentile Renka 1 of 4 in class of 60 students. Find 60-4 = 933 7 93.3% Rank percentile conk, Bob has class rank total -CR total o Bob has 93,3% hank, what is his class rank? total -CR=% conl (total) 60-CR = 1933(60) CR=4.02 of 12, Find: 1. Mean of 65 SD A. Q2 = 0 Bi Pi6 = 16% fall below cutpoint ,347-100 = *65 4(12) +65 53 65 1 x C. Pq4 .34 → 1000- 2 1112]+65 - 77 D. Ds = 165] 2. Mean 100 SD 15 # of Students 1500 A How many students scored between 85-115? z= 25-100 -18,3413 LONA) 15-400 = 1 =,3413 16826 ->,6926C1500) = 1023,4 students 65 160 IIS B. How many students scored between 70 and 130? Z= 70-100 = 2 , 4772 z= 130-100 = 2 ,4772 .9544 →,9544(500) = 1431.6 stuelents C. How many students scored above 145? - 5000 Zz 145-100 = 3 + 4987 C.00137,00131500)=1,95 -> (2 students] T ! 145 Study Soup 3, 10,000 students mean 500 SD 60 A student scoring below 440 points was deficient in math. How many students were deficient? ,5000 Z = 440.500 | 3413 1587 (10,000) 1587 students 440 500 4. In a class of 25, Bill has a rank of 25. What percentile is a he ? 0% 5. Jill was 80th in class, but has a the higher class a class percentile rank of 200. Nathan is in the same rank of 80, which student has tolal-Ch = % cant Itotal) Nathan → 200-CR=;80(200) CR-40 6. John scored 572, mean 400 SD 112 Ber scored 28 on ACT mean 14 7 51 5 to Z2 572-400 = 1,54 7,4382 13) 7=28=18 = 2 ->,4772 Bev 400 572 7. Test Test 2 Test #3 I mean 66 50 4 mean 66 SD 2 men 92 SD 6 Ai Maria took Test #lo scored 70; Who did Better? Janette took Test #28 Scored 70, 66 70 Z= 20-60 ch Z= 70-666 = 2 B. Adrian scored 68 on Test #2. Julio scored 68 on Test # 3. Who did better? 68-66=1 68-72 067 [Adrian 8. median 500 50100 16th of of 400 Ai and 50th percentile - 500 B. Find 84th percentile 500 50 , → +34 1 s .99 = Too 1996100) +500 599 599 > 9. Meg was ranked 25th in her class of 250. What is her percentile renk? total -CR total 90% 10. Class of so. Cathy has to rank of 60. What is her class rank? total-CR=% rank (total) 50-CR-,60(50) (R = 20 1. If the the distribution distribution has if the the third SD is quartile of 45, what is the 10? mean of (15 1125 ) ► look inside out for z of 125 2 = 68 x 45 de 43120 618-45 - mean mean= 38.2 mean = 45-68 Comparisons Jack scored 72 out of 110 Mary scored 87 out of 210 Bill scored 51 out of 65 2-72-81=-68 Z=87067 = 116 65,5% 41,4% 78,5% mean 81 so 5 mean 67 SD12 mean 57 soa Jack Bill o -Z mary +Z T-score T-score = Z (10) + 50 man STEN (standard ten Z(2) +5.5 Jacks -118/10) +50=32 Maryi 116 (10) + 50 = 66 Bill' 4,67(10) + 50 = 43.3 Starine (standard nine) Z (2) +5 SD Formula Z- cutpoint mean Cotport mean Formula hey mean t-score o T-score 50 STEN 5,6 STANINE 5 10 2 2 Z(10) +50 Z(2) +5.5 Z(2) +5 * mean + SD are always the same for each type of score * Examples Calculate T-score, -2010)+50 = 307 Calculate STEN. -212) 45,5 = [1.5 Calculate STANINE. -262) +5 - 2) Determine the stanne for the 70th percentile, 700% inside out on chart for 2 Z=152 ,52(2) +5 = 6.04 3) Determine the stanine for the 44th percentile, 4402 Bu yay inside out for a inside out for 106 Z=15 . 15(2)+5 = 5.3 for each of the Z-score test scores and evaluate the relative 4) Determine the standing 81 - 74,3 A did better A A Test Ai mean B. Test B: mean 74.3,50 3,6; test score 81 720; SD 146, test score 840 Z= 0 = 1,86 2: 3904720 - 82 B) Test Ai mean 3.1; SD 211; score 28 z= 22 -14 A did better 5.3-6.2. re 5,3 Ze 5.3-6. -5.3 Boxplats Low 2 High 15 edian 8 - Set Al 2 344667 15 Set B i 236 689 12 14 15 Set ci 245813 15 Set Di 236689101115 of first half the second half Find medion, then median Outliers clearly marked w/ * Cathers LL = lower limit UL = upper limit median 450 Q, 300 Q2 700 LL LQ - 1,5 (Q 3-Q,) LL 2300-1.5 (700-300) LL300-600 9LL 6-306 Percentile Rank UL7 Q3 +1.5 (Q2-Q) UL 7700+ 1.5 1700-300) UL > 700+ 600 UL 7 1300 - Class Rank & total - class rank = percentile rank total 25-11-14 .56 $6th percentile 56% fall below him Companha_Student Scores Find Z-scores for each student and compare Percentiles meand median = 500 SD = 100 16thol is 400 A. Find 50th percentile 500 B. Find 84th percentile. 1/2 of 68% 34% + 15D mean + ISD 500+ 1 (100) 500 +100 hod 56% 34% 8) A car is advertised is $14, 400, what If the at is a the 15% sale original discount. price ? price X 14,400 95 BD 1312, 240 Exam 3 Study Guide Word Problems Sections I. Dimensional Analysis I. Pan Scales I Strip Diagrams I. Unit hate Double Number Line Vi Coins" or Mixture Problems II. Work Word Problems Part of Whole. VII. Distance Word Problems VIT, Percents and proportions I. Dimensional Analysis * must go step by step to cancel units * D) How many seconds are there in a day? Aim: sec/day 60 sec x 60 min x 24 hr - 186, 400 seconds per day 1 mith 1 Wr 1 day 2) You have $7.25 in quarters, How many quarters do you have? Aim: Quarters $125 x 4 quarters - [ 29 quarters] I. Pan Scales 1) Illustrate 5x+1 = 3x + 7 using pan scales, IL H 323 2) What does the large box equal ? I Strip Diagrams 1 The Ratio of Bill's cards to Kevin's is 14 to 6. After Bill gives 12 cards to thevin, they have an even number of cards. How many cards did Kevin have originally ? Kevin If you add 4 boxes, they. are even III = 12. Cards L = 3 12+ 4 = 3 cards 6:3=18 Kevin had 18 cards! 2) A bakery sold 3/gths of the muffins. The cemaining muffins a were divided equally among 3 employees. Each employee. got lle muffins How many muffins did the bakery have originally? W x # of muffins 127-16 sold ! 3/6x sold — 2/5x remaining The bakery Originally had 120 muffins 1x = 1 2x= 240-7X=120 I Whit Rate / Double Number Lines * Pay Attention to the relations of variables e As X raises, does Y increase or decrease? 1) It costs $30 for 6 books. What is the unit rate ? SENSOR 30 + 6=5 $5 is the unit rated 2) Rich cuns 5 meters every 2 seconds, A. Using a double number line, what is the unit rate? XqYq meters. 5125 12.5 meters per second seconds) 211 +2 B. How long will it take to run 24 meters ? meters 5124 19,6 seconds Second 2916 24.8 Study Sky I Can" or Mixture Proplems * value & amount * 1) A wallet contains the same number of pennies, nickels, and dimes, The coins total $1,44. How many of each con are there? X= # of cons Ola +.05x + 10x = 1,44 116% = 144 x=91 >.01() + .0509) +,1019) = 1.44 1.09+, 45+,90 = 1,44 ✓ 2) A collection of 33 coins consisting of nickels, dimes, and quarters, has a value of $3.30. If there are 3 times as many nickels as quarters, and one-half as many dimes as nickels, how many of each kind of con are there? X= # of quarters 3 x=# of nickels 15(3x) = # of dimes 125x 5,05(3x) + .5(3x)[.10] -3.30 .25%+ ,15% 1,15% = 3.30 . 55% = 3.30 x = 6 quarters Bx= 18 Mickels 1508) = q dimes ] 3.30 ~ 3) Your school is holding an event selling adult tickets for $5 each and children tickets for $2.50. A total of 548 tickets have been sold for a total of $2,460. How many adult and children tickets have been sold? X= # of adult tickets 548-X = # of children tickets 5x + 2,50 (548-x) = 2, 460 5x + 1370-2,5%= 2,460 2.5% = 1090 L X= 436 adult tickets 1548-436 = 112 children tickets + 1.50 ,90 4) Brand x sells 2l0z bags of mixed nuts that contain 29000 peanuts, To make the product, they combine Brand A which contains 35% peanuts and Brand B which contains 25% peanuts, How much do they need to use of each brand? Brand X = 29%, Brand A- 35%, Brand 8 = 25000 21 oz x amount of Brand A 21 - x= amount of Brand B 29120) = 35x + 25(21-X) 609 = 35% +5.25 -25% 84 = 10% - x = 8.4 oz of Brand A T 22- x = 12,6 oz of Brand B . Working World Problems: * Part of the whole * 1 Working alone, Ryan can dig a loft by loft hole in 5 hours, Cass "can dig the same hole in bo how's. How long itzuld it take them if they worked together? Ryan Cass' Part 1 Wiele 5 tūs Box -> 6x + 5x = 30 lx - 30 x=2.73 hours) 2 Working together, Paul and Dan can pick 40 bushels of apples in 4,95 hours. Had Dan done it alone, it would have taken him 9 hours, How many hours would it have taken Paul alone ? Part It I Whole ( x q I x x 9.4,95 = 914,95) + 4,957 = 9x 4.951 1 44.55 = 4.05% X = 11 hours VII. Distance Word Problems *D=RT, R = 7, T = 2 * 1) A 555 mile 5 hour plane trip was flown at two speeds. For the first part, the average speed was 105mph. Then the tailwind picked up and the remainder of the trip was flown at an average speed of 115 mph. For how long did the plane fly at each speed? 1st 2nd 105T 105 115 (5-7) 115 T 5-T 105T +115(5--T) = 555 105T+ 575-115T = 555 10T=20 T= 2 I 1st part flown for 2 hours L and part flown for 3 hours 2) A car and a bus set out at 2 pm from the same point, headed in the same direction. The average speed of the car is 30mph slower than twice the speed of the bus. In two hours, the car is 20 miles ahead of the bus. Find the rate of the car. R D R I 212x-30) = 2x+ 20 car 2(2x-30) 2x-30 2hr. - 40-60 = 2x+ 20 bus 2x 2h 2x = 80 - x= 40mph bus 12x-303 50 mph card VIII. Peccents and proportions. 1) At Little Rock number is School, 476 65% of the students ride their bikes to school. school encollment, how many students If this are enrolled? 476= 165 of students 476 = 165* X2477,65 → = 732.31 Students enrolled 2) Anne works in a supermarket for $10/hr. If her pay is increased $12/hr, what is the % increase in pay? Sloths $12/hr %A-170- 52 = 20% increase to

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