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# MTH 157 Week 1 Checkpoint

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Date Created: 11/06/15

Section 81 2 a Frequency table Score Difference 49 b Frequency 1 NO IO I L LcnmmngANANAAAAAA Relative Frequency Table Score Difference 49 45 3o 29 28 23 22 2o 18 17 16 14 13 12 1 1 9 8 6 Frequency 1 AmmmgwwANANAAAAAA Relative Frequency 2 mQQNbNPNNNNNN LL NO D 5 1 2 4 5 1O 2 5 1O 1 2 4 C Stem and leaf plot 01122222444445688888899999 11122223334446778 2 O O 2 3 8 9 3 O 4 5 9 d Histogram Score Differences 14 12 ile E 3 3 Dquot 4 va 2 I m I I L 115 aim iii15 lie2e 2125 zeEltl Elli35 3541 4145 4658 Difference 8 The total numbers of students would double because the amount of grades doubled Since the amount doubled the ratio of the grades would not change Each grade was being increased by the same factor 2 Therefore the graph would not change since the ratiopercent did not change 18 This graph shows what is considered a quotfair pricequot for gasoline in many different countries across the world The quotfair pricequot differs from country to country this is because each country has different factors that contribute to this price As noted from the graph the price of gasoline in countries such as Germany and South Korea are substantially higher than in Australia or Canada In Canada and the United States the demand for cheap gas is higher because of how much driving they do in the country based upon the long distances travelled The country with the highest quotfair pricequot is the United Kingdom with 516 per gallon The country with the lowest quotfair pricequot is the United States with 199 per gallon 22 For this set of data I would use a bar graph A bar graph displays data that can be divided into can many categories The bar graph can show the category on one axis and the level of stress on the other this would make reading each category s level extremely easy Stress Units of Life Experiences 1213 m IUD so x if so I g g I 21039 1 w E quota quotIt a g V I 1 Q 395 t l e s quot15 5 a g V E Q 9 if 9 n L2 39 Life Experience 24 I would use a stem and leaf plot to display this data By rounding the price to the nearest hundred dollars we are able to attain accurate and ef cient numbers A stem and leaf plot is the best way to display this information because you can be split the data into extreme categories Additionally it would be easy to group many numbers into these categories These numbers can also be easily compared to each other and analyzed if needed Each category represents the dollar value expressed in thousandths of dollars Each number in the category indicates the hundred dollar value associated with the thousand dollar category For example 87 represents 8700 Dollar value in thousandt Dollar value in hs Hundredths 8 I 7 9 9 1o 11 12 13 14 15 16 17 3 5 18 19 1 5 6 2o 21 5 8 22 23 24 25 26 27 8 28 o 29 30 Section 82 mmooo 2 Salmon Catch Lengths at Bonneville Dam 16 1d v Nlumlbew of Fllslh TI CG TU FUFg EUBg g gg 1DU1U911U 119 119 Length 1111 6 Using the best t line I would predict that if a student has an ACT score of 25 then the average would be 80 If the average were 60 I would predict an ACT score of 15 12 This chart shows the process average based off of a sample of parts and products In order for a process to meet quality control speci cations it must be within 125 of the process average If a process is above or below the action limits 125 of the process average then the process does not meet quality control speci cations Currently the process average is 10 our process falls within the range of 10125 and 09875 therefore our current process is meeting quality control speci cations 14 I would use a bar graph to display this data A bar graph can easily organize the data and is easy to read First I would label the horizontal axis of the graph with the age into 5 categories Now I would label the vertical axis with the death rate in thousands This would range from 0 to 18 leaving room for the lowest point 46 and the highest point 157 The bars would extend out vertically upward that is the bar would start at 0 deaths and go up to the death rate for the speci c category Section 83 2 Ea Ell9 1 1 2 15 15 2 23 V The mean IS the average 1 13 11 2 2 11 The median is the middle number The mode is the most frequent number 15 The midrange is the point midway between the high and low point 1 8 3 35 3 a Mean T E Medbn80 Mode80 b All the averages will yield the same result 80 Therefore Doug has no preference c An average of 84 will result in a total score of 2420 Currently Doug has a total score of 3039 m4 32039 In order to get an average of 84 Doug has to get a 100 on his next test 420 320 100 The likelihood of this happening is very low considering the highest score Doug has gotten is an 85 12 Range change from high to low 96 1392 2 24 Interquartile Range the difference between the third and rst quartile 6639 BD 16 32 3 3 32 x ElEEli 9 96 Mean 64 Variance 16 16 4 16 36 146 6311 Standard Deviation x 53317 2 1313 20 a As shown in the graph team C has the greatest range 95 13 82 Team B has the smallest range 72 5 67 b The team with the largest interquartile range is team C 85 40 45 The team with the smallest interquartile range is team B 48 30 18 c The team with a mean that is closest to its median is team B The median in this case is 40 and the mean 385 H 365 This can also be seen from the graph since the boxes are nearly symmetrical across the median for team B d Team A would likely have a mean farther away from its median As shown from the graph the boxes are nowhere near symmetrical whereas the boxes for Team B and C are close to symmetrical 22 The range is the difference between the highest and lowest point 57 29 28 The youngest person would be 28 years old 36 The interquartile range does not have to be less than the range For example it could be equal to the range as shown in the following situation 1 1 2 3 4 5 5 The range in this situation is 5 1 4 The interquartile range is also 4 Q3 Ql 5 1 4 Ql 1 Median 3 Q3 5 Section 84 4 This statistical analysis is based off of limited facts In order to give a generalization you would have to consider all of the airlines that y to Normal You cannot just base the facts on one airline because there is nothing to compare it to Therefore how would you know that most people prefer American airlines 10 Yes this claim can be correct If we look at the extreme cases in each scenario we will notice that for poultry dogs can have as high as 170 calories whereas meat and beef can have as low as 110 calories In these extreme cases poultry dogs do have 150 more calories than meat and beef can Therefore although extreme this statement can be correct Chapter 8 Review 2 Histograph 19 12 13 E t ESDtU 999t 959t 9 t 959t S t SSDtU EDDtU BSUtU F t FSDtU 299 299 999 999 999 999 599 599 E99 E99 F99 999 Frequent l S T cnre Pie Graph Scores 21 99999799 29999299 299 F59tg999 ESDtUEQQ The histograph provides a better explanation for the score distribution The histograph shows the change from scores in a bell curve fashion low to high to low This gives us a better view of the grade distribution The pie graph is harder to visualize how the grade is distributed as the score increases A pie graph is better used with percentages and with a smaller amount of categories 6 Many people will want to vote with their opinion but not everyone would want to spend their own money to vote therefore the results would be biased 8 I believe that the median income should be used Averageville may have outliers that could dramatically shift the mean one way or the other If a billionaire lived in Averageville the mean would be dramatically shifted and would not resemble the town s average income In this situation the median would be more useful In a situation with no outliers the median would still be useful because the mean and median would be extremely close as the income would be normally distributed throughout society 14 I would look at the company s average mean life In this situation the light bulbs are being bought in large quantities and in doing such we would expect the average life to be long In order to maximize that average we would use the mean NCTM Standards According to the NCTM the data analysis and probability standard for students from grade 6 to grade 8 states that students should be able to select create and use appropriate graphical representations of data including histograms box plots and scatter plots In this homework assignment creating and selecting different types of graphs that would best be used for the set of data met this standard Another standard that I met was the number and operations standard for students from grade 6 to grade 8 This standard states that students should develop and use strategies to estimate the results of rationalnumber computations and judge the reasonableness of the results The question in regards to the ACT score we had to estimate the class average of a student

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