Statistics Questions

Which best expresses a potential difficulty with preference ballots 1 point Because preference ballots are so rare it is easy to forge extra copies of them and vote illegally Preference ballots only work in two candidate races and most races have at least three candidates Preference ballots are easy to understand but hard to produce and distribute to polling places OFilling out a preference ballot for each position being voted on can be time consuming

10 A travel agent is booking a trip to England Scotland Ireland and France for a group of senior citizens and created the shown preference schedule from data gathered from them E England I Ireland S Scotland F France The agent is recruiting more seniors to join the group How many seniors would the agent need to recruit to create a majority that wants to visit France first number of votes 15 12 16 19 1st 2nd 3rd 4th F EEI E S S S ISE F F F The agent needs to recruit 17 additional people The agent needs to recruit 17 additional people who want to visit France first The agent needs to recruit 33 additional people of whom 17 want to visit France first The agent needs to recruit 33 additional people who want to visit France first 1 point

9 A travel agent is booking a trip to England Scotland Ireland and France for a group of senior citizens The agent sent surveys to the group asking which countries they would like to visit in order and created the shown preference schedule E England I Ireland S Scotland F France Which country is the Condorcet winner number of votes 15 12 16 19 1st 2nd 3rd 4th Scotland Ireland England France FEEI ESIS SISE I F F F

Which of the following best describes a problem that occurs when the plurality method is used 1 point The plurality method only allows comparisons between pairs of candidates and can t be used when there is an uneven number of candidates O The plurality method sums the votes from all choices which takes a long time and can get confusing there are a lot of candidates to choose from O The plurality method only considers the first choice line which leaves out many factors that could affect the outcome of the vote The plurality method only considers the first choice and second choice lines which often vary considerably from subsequent lines

5 Suppose this preference schedule gives the results of an election between three candidates Amy A Beth B and Candice C Based on the plurality method who is the winner of the election number of votes 20 19 5 1st 2nd 3rd CBA BAB ACC O Amy A Beth B Candice C No candidate wins using the plurality method

6 22 Standard Normal Use a table or technology to answer each question Include an appropriately labeled sketch of the Normal curve for each part Shade the appropriate region a Find the probability that a z score will be 1 00 or less b Find the probability that a z score will be more than 1 00 c Find the probability that a z score will be between 0 90 and 1 80

6 5 Loaded Die Example 2 A magician has shaved an edge off one side of a six sided die and as a result the die is no longer fair The figure shows a graph of the probability density function pdf Show the pdf in table format by listing all six possible out comes and their probabilities Probability 0 25 0 20 0 15 0 10 0 05 0 00 1 2 3 4 Outcome on Die 5 6

6 1 6 4 Directions Determine whether each of the following variables would best be modeled as continuous or discrete 6 1 Example 1 a Number of cars passing a certain patrolman during one working day

Solve the following problems involving complex numbers Show all work Put your final answer on the line provided 6 7 2 6i 2 6i 10 2i

Create a table and graph the equation y Is it a function Explain why or why not

as needed Determine the domain and range using the indicated notation and whether or not the equation is a function 1 Set notation f x 3x 51 2 Interval notation x 4 Domain Range Function Y N Domain Range Function Y N

4 What is the difference between an expression equation 5 What two parts make up a complex number

Solve the following problems involving radicals 10 5 3 3 3

A data set of values has a mean of 45 and standard deviation of 5 The z score for a point A is 0 The z score for a point B is 0 2 State the value of point A State the value of point B type your answer type your answer

13 Given the preference schedule below how many points does the Borda count winner receive 1 poi number of votes 9 56 1st 2nd 3rd 4th 50 056 057 059 ABC CAD BDB DCA

12 Which of the following values for x will result in a total Borda count of 8 for candidate 13 for candidate C number of votes 3 2 x 1st 2nd 3rd 04 3 ACB CAA BBC

4 The Great Chili Cook off is underway In preliminary voting Jerry Carol and Dante impressed the judges Based on the judges preference schedule which of the following is the Borda winner for this round of the cook off number of votes 3 1st 2nd 3rd 4th Carol Dante George Jerry 5 4 Dante Carol Jerry Jerry Dante George Carol George Carol George Jerry Dante

15 The preference schedule shown was used to choose the finalists for a talent contest The contestants are Dana August Cameron and Belinda Based on the Borda count who will be in first place going into the finals of the talent contest number of votes 4 5 6 7 1st 2nd 3rd August Belinda Cameron Rana DACB ACBD BDAC

Results from a one way ANOVA indicate that there is not significantly different effect of gender on baseline self compassion F 1 96 effect size np2 125 3 1299 09 P 135 Tukey post hoc analyses indicated that those who identified as Males were type your answer in self compassion than Females p type your answer Males were type your answer Males were type your answer in self compassion than Nonbinary individuals p type your answer self compassion than Transgender individuals p type your answer Females were type your answer in self compassion than Transgender individuals p type your answer See Table 1 for means and standard in self compassion Nonbinary individuals p Nonbinary Females were type your answer in self compassion than Transgender individuals p type your answer type your answer individuals were type your answer deviations Table 1 Means and SDs for Self compassion Among Different Gender Identifications Condition Mean Male Female Nonbinary Transgender 76 82 54 17 72 09 75 64 Standard Deviation 26 29 15 51 30 41 26 58 Submit in

Consider this preference schedule Is there a candidate who could be considered the plurality winner and the majority winner number of votes 14 10 11 1 111 1st 2nd 3rd 4th BCAAC AACD D CDDCA DBBBB Yes candidate B ONo none of the candidates have exactly 50 of all available votes ONo a candidate cannot be both a plurality winner and a majority winner OYes candidate C

1 Suppose you and your friends want to go snowboarding There are four excellent places to go Diamond Bar D Big Boulder B Arrowhead A and Camelback C You ask your friends to rank the locations from their most preferred to their least preferred and compile the responses in a preference table Which location was ranked first by most of your friends 11242 1st ADA BA 2nd D B BAD 3rd BAD CC 4th CCCDB O Arrowhead Big Boulder Camelback Diamond Bar

2 What percentage of voters who cast a preference vote in this election put Brown in first place 1 point 19 9 11 14 1st Adams Brown Brown Carter 6 2nd Brown Carter Adams Adams 3rd Carter Adams Carter Brown 11 017 034 O 50

2 Using the Two Way Frequency Table below answer each question in whole number format or simplest fractional format Male Female Total High School Diploma 16 28 Bachelor s Degree 46 51 Master s Doctoral Degree 3 6 Total 65 a 2pts How many females earned Diploma or Degree b 2pts Probability of a female earning a Bachelor s Degree c 2pts How many males earned a Master Doctoral Degree

1 Using the Two Way Frequency Table below answer each question in decimal format to the nearest 10ths Male Baseball Basketball Football 13 23 15 16 20 31 13 Total Female Total 36 100 a 3pts Choosing a student at random what are the chances of selecting a female student and a basketball player b 3pts Choosing a student at random what are the chances of selecting a male student or a football player c 3pts Choosing a student at random what are the chances of selecting a female student and a football player 33 48 52

wait time in the drive thru for each Assume it is known that the population standard deviation of the wait times in the drive thru for the hamburger chain s restaurants is 2 91 minutes Based on your sample follow the steps below to construct a 90 confidence interval for the population mean of the wait times in the drive thru for all customers Then state whether the confidence interval you construct contradicts the restaurant chain s claim If necessary consult a list of formulas a Click on Take Sample to see the results from your random sample of 40 customers Take Sample Sample size 0 Point estimate 0 Population standard deviation 0 Critical value 0 Compute Enter the values of the sample size the point estimate for the population mean the population standard deviation and the critical value you need for your 90 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute 0 00 Number of customers 40 F 0 00 Sample mean 2 00 4 36 4 00 Sample standard Standard error Margin of error deviation 90 confidence interval 5 00 2 52 6 00 b Based on your sample graph the 90 confidence interval for the population mean of the wait times in the drive thru for all customers Enter the lower and upper limits on the graph to show your confidence interval For the point enter the restaurant chain s claim of 4 13 minutes 90 confidence interval Population standard deviation 2 91 O No the confidence interval does not contradict the claim The restaurant chain s claim of 4 13 minutes is outside the 90 confidence interval 8 00 O No the confidence interval does not contradict the X claim The restaurant chain s claim of 4 13 minutes is inside the 90 confidence interval O Yes the confidence interval contradicts the claim The restaurant chain s claim of 4 13 minutes is inside the 90 confidence interval X Critical values 20 005 2 576 20 010 2 326 20 025 1 960 O Yes the confidence interval contradicts the claim The restaurant chain s claim of 4 13 minutes is outside the 90 confidence interval 0 050 1 645 0 100 1 282 c Does the 90 confidence interval you constructed contradict the restaurant chain s claim Choose the best answer from the choices below 5 5 10 00 10 00 BE A

To determine the possible effect of a chemical treatment on the rate of seed germination 300 chemically treated seeds and 275 untreated seeds were sown It was found that 270 of the chemically treated seeds and 239 of the untreated seeds germinated Let be the proportion of the population of all chemically treated seeds that germinate and let be the proportion of the population of all untreated seeds that germinate Find a 99 confidence interval for p p2 Then find the lower limit and upper limit of the 99 confidence interval P2 Carry your intermediate computations to at least three decimal places Round your responses to at least three decimal places If necessary consult a list of formulas Lower limit Upper limit 0 X

In random independent samples of 300 adults and 400 teenagers who watched a certain television show 168 adults and 272 teens indicated that they liked the show Let p be the proportion of all adults watching the show who liked it and let P2 be the proportion of all teens watching the show who liked it Find a 90 confidence interval for P P Then find the lower limit and upper limit of the 90 confidence interval Carry your intermediate computations to at least three decimal places Round your responses to at least three decimal places If necessary consult a list of formulas Lower limit Upper limit 0 X

What does one assume when using the relative frequencies of past events to predict future events For example hen calculating the probability of a student passing the next assignment in a course question 1 what did you ssume about the conditions in the past and the future

5 The table below shows the percentage of females in the U S labor force at various times throughout history Years after 1900 Percentage 50 29 6 60 33 4 90 45 3 70 80 38 1 42 5 a Find the regression line for the data above Round to the nearest hundredth b Use your equation to predict the percentage of women working in 2010 Round to the nearest tenth of a percent 100 52

For a study conducted by the research department of a pharmaceutical company 270 randomly selected individuals were asked to report the amount of money they spend annually on prescription allergy relief medication The sample mean was found to be 17 60 with a standard deviation of 5 30 A random sample of 225 individuals was selected independently of the first sample These individuals reported their annual spending on non prescription allergy relief medication The mean of the second sample was found to be 18 40 with a standard deviation of 4 50 As the sample sizes were quite large it was assumed that the respective population standard deviations of the spending for prescription and non prescription allergy relief medication could be estimated as the respective sample standard deviation values given above Construct a 95 confidence interval for the difference between the mean spending on prescription allergy relief medication and the mean spending on non prescription allergy relief medication Then find the lower limit and upper limit of the 95 confidence interval Carry your intermediate computations to at least three decimal places Round your answers to at least two decimal places If necessary consult a list of formulas Lower limit Upper limit X

In a comparative study of two new drugs A and B 400 patients were treated with drug A and 350 patients were treated with drug B The two treatment groups were randomly and independently chosen It was found that 280 patients were cured using drug A and 252 patients were cured using drug B Let p be the proportion of the population of all patients who are cured using drug A and let p2 be the proportion of the population of all patients who are cured using drug B Find a 99 confidence interval for P P Then find the lower limit and upper limit of the 99 confidence interval Carry your intermediate computations to at least three decimal places Round your responses to at least three decimal places If necessary consult a list of formulas Lower limit Upper limit X

A random selection of volunteers at a research Institute has been exposed to a weak flu virus After the volunteers began to have flu symptoms 10 of them were given multivitamin tablets daily that contained i gram of vitamin C and 3 grams of various other vitamins and minerals The remaining 10 volunteers were given tablets containing 4 grams of vitamin C only For each individual the length of time taken to recover from the flu was recorded At the end of the experiment the following data were obtained Treated with 4 2 2 8 3 5 6 3 4 6 1 4 6 2 6 3 4 3 4 9 multivitamin Treated with vitamin C Send data to calculator Days to recover from flu 5 3 4 5 2 2 4 1 4 7 3 7 1 7 5 3 5 2 5 1 Lower limit Upper limit Send data to Excel Suppose that it is known that the population standard deviation of recovery time from the flu is 1 8 days when treated with multivitamins and that the population standard deviation of recovery time from the flu is 1 5 days when treated with vitamin C tablets Suppose also that both populations are approximately normally distributed Construct a 90 confidence interval for the difference between the mean recovery time when treated with multivitamins and the mean recovery time when treated with vitamin C only Then find the lower limit and upper limit of the 90 confidence interval Carry your intermediate computations to at least three decimal places Round your answers to at least two decimal places If necessary consult a list of formulas X

Cigarettes smoked Tumor Size TV 17 02 0 8 9 10 11 12 13 14 15 1 3 2 5 4 1 6 2 6 1 9 4 10 5 12 0 13 1 14 5 15 9 16 7 18 2 1 Graph this dataset on the scatter plot above 2 Describe the relationship between these two variables Cigarettes Smoked Tumor Size

P2 A random sample of 225 bolts from machine A contained 18 defective bolts while an independently chosen random sample of 200 bolts from machine B contained 14 defective bolts Let be the proportion of the population of all bolts from machine A that are defective and let be the proportion of the population of all bolts from machine B that are defective Find a 90 confidence interval for p p Then find the lower limit and upper limit of the 90 confidence interval Carry your intermediate computations to at least three decimal places Round your responses to at least three decimal places If necessary consult a list of formulas Lower limit Upper limit X

An engineer wants to know if producing metal bars using a new experimental treatment rather than treatment makes a difference in the tensile strength of the bars the ability to resist tearing when pulled lengthwise 0 10 answer parts a through e Assume the population variances are equal and the samples are random If convenient use technology to solve the problem Treatment Tensile strengths newtons per square millimeter Experimental 437 404 394 359 446 361 385 Conventional 401 363 436 387 437 431 429 369 400 415 a Identify the claim and state Ho and Ha The claim is The new treatment What are Ho and Ha The null hypothesis Ho is Which hypothesis is the claim O The null hypothesis Ho O The alternative hypothesis Ha b Find the standardized test statistic The alternative hypothesis Ha is in the tensile strength of the bars Type an integer or decimal rounded to the nearest thousandth as needed c Decide whether to reject or fail to reject the null hypothesis the null hypothesis d Interpret the decision in the context of the original claim At the 10 significance level there is not enough evidence to support the claim

gium is less a E Accordi to the historical data the life expectancy than the life expectancy in the United States A new study has been made to see whether this has changed Records of 250 individuals from Belgium who died recently are selected at random The 250 individuals lived a mean of 78 3 years with a standard deviation of 7 years Records of 265 individuals from the United States who died recently are selected at random and independently The 265 individuals lived a mean of 76 6 years with a standard deviation of 6 2 years Assume that the population standard deviations of lifetimes in these two countries can be estimated by the sample standard deviations as the samples used were quite large Construct a 95 confidence interval for the difference between the life expectancy in Belgium and the life expectancy in the United States Then find the lower limit and upper limit of the 95 confidence interval Carry your intermediate computations to at least three decimal places Round your answers to at least two decimal places If necessary consult a list of formulas Lower limit Upper limit X S Aa

The contingency table shows a random sample of engineering psychology and biology articles and if and how they were coauthored At a 0 10 can you conclude that the subject matter and coauthorship are related Complete parts a through d The Coauthorship Coauthored Internationally coauthored Not coauthored a Identify the claim and state the null and alternative hypotheses Ho Coauthorship and subject matter are Ha Coauthorship and subject matter are is the claim Subject matter Engineering Psychology Biology 42 43 48 22 15 40 35 D b Calculate the test statistic If convenient use technology x Round to three decimal places as needed c Decide to reject or fail to reject the null hypothesis Then interpret the decision in the context of the original claim What is the conclusion of the test Ho There How does this relate to the original claim enough evidence to support Ha 9 40 O A This supports the claim that subject and coauthorship are not related OB This supports the claim that subject and coauthorship are related OC This does not support the claim that subject and coauthorship are related This does not support the claim that subject and coauthorship are not related

3 The linear model that goes with this dataset is Plant Height 0 267 Petal Length 4 533 Interpret the slope and y intercept of this linear model in context Lai isbam

3 The linear model that matches this dataset is Tumor Size 1 017 Cigarettes Smoked 0 293 Interpret the slope and y intercept of this linear model in context

Find the equation of the regression line for the given data Then construct a scatter plot of the data and draw the regression line The pair of variables have a significant correlation Then use the regression equation to predict the value of y for each of the given x values if meaningful The number of hours 6 students spent for a test and their scores on that test are shown below Hours spent studying x 1 Test score y 38 80 0 Hours studying y x Round the slope to three decimal places as needed Round the y intercept to two decimal places as needed Choose the correct graph below A O B 1 2 4 4 5 12 43 51 48 64 72 G OA 63 4 OB 50 5 OC 131 1 80 Hours studying Q G O C Test score 80 a Predict the value of y for x 3 Choose the correct answer below 0 Hours studying OA 50 5 OB 53 7 OC 63 4 OD not meaningful b Predict the value of y for x 4 5 Choose the correct answer below a x 3 hours c x 15 hours D not meaningful c Predict the value of y for x 15 Choose the correct answer below OA 131 1 OB 53 7 OC 63 4 OD not meaningful d Predict the value of y for x 2 5 Choose the correct answer below b x 4 5 hours d x 2 5 hours D 80 0 Hours studying 5

surgery durations for all brain tumor patients is 3 13 hours You are a data analyst for a health insurance company and want to test that claim To do so you select a random sample of 32 brain tumor surgery patients and you record the surgery duration for each Assume it is known that the population standard deviation of the durations of all brain tumor surgeries is 1 68 hours Based on your sample follow the steps below to construct a 95 confidence interval for the population mean of the surgery durations for all brain tumor patients Then state whether the confidence interval you construct contradicts the medical group s claim If necessary consult a list of formulas a Click on Take Sample to see the results from your random sample of 32 brain tumor patients Take Sample Sample size Point estimate 0 Population standard deviation 0 Critical value 0 Enter the values of the sample size the point estimate for the population mean the population standard deviation and the critical value you need for your 95 confidence interval Choose the correct critical value from the table of critical values provided When you are done select Compute Compute 0 00 Number of patients 32 0 00 Sample mean 2 00 3 36 Sample standard deviation 1 66 4 00 Standard error Margin of error 95 confidence interval b Based on your sample graph the 95 confidence interval for the population mean of the surgery durations for all brain tumor patients Enter the lower and upper limits on the graph to show your confidence interval For the point enter the medical group s claim of 3 13 hours 95 confidence interval 5 00 6 00 No the confidence interval does not contradict the claim The medical group s claim of 3 13 hours is inside the 95 confidence interval O No the confidence interval does not contradict the claim The medical group s claim of 3 13 hours is outside the 95 confidence interval Population standard deviation 1 68 Yes the confidence interval contradicts the claim The medical group s claim of 3 13 hours is inside the 95 confidence interval 8 00 O Yes the confidence interval contradicts the claim The medical group s claim of 3 13 hours is outside X Critical values 20 005 2 576 0 010 2 326 20 025 1 960 F0 050 1 645 20 100 1 282 X c Does the 95 confidence interval you constructed contradict the medical group s claim Choose the best answer from the choices below 10 00 10 00 5

The coefficient of determination r is the ratio of which two types of variations What does r measure What does 1 r measure The coeffcient of determination is the ratio of the explained variation to the total variation OA The coefficient of determination is the ratio of the OB The coefficient of determination is the ratio of the total variation to the explained variation explained variation to the total variation OC The coefficient of determination is the ratio of the D The coefficient of determination is the ratio of the total variation to the unexplained variation unexplained variation to the total variation Choose the correct answer below O A The coefficient of determination is a measure of O B The coefficient of determination is the percent of how closely two variables vary together the variation that is unexplained OC The coefficient of determination is the percent of O D The coefficient of determination is the percent of variation of y that is explained by the relationship the predicted values that equal the actual data values between x and y Choose the correct answer below OA The value 1 r2 is the percent of the predicted values that equal the actual data values OB The value 1 r2 is the percent of the variation that is unexplained OC The value 1 r2 is the percent of variation of y that is explained by the relationship between x and y OD The value 1 2 is a measure of how closely two variables vary together

A manufacturer withdrew Drug V from the market after a study revealed that its use was associated with an increase in the risk of heart attack The experiment was placebo controlled randomized and double blind Out of 1287 people taking Drug V there were 47 heart attacks and out of 1283 people taking the placebo there were 24 heart attacks Perform a hypothesis test to test whether those who take Drug V have a greater rate of heart attack than those who take a placebo Use a level of significance of 0 01 Can we conclude that Drug V causes an increased risk of heart attack Determine the hypotheses for this test Let p represent the population proportion of heart attacks for those who take Drug V and let p represent the population proportion of heart attacks for those who take the placebo Choose the correct answer below OA Ho P SP2 Ha P P2 O D Ho P1 P2 Ha P P2 Find the test statistic for this test O Reject Ho O Do not reject Ho OB Ho P1 P2 Ha P1 P2 O E Ho P1 P2 Ha P1 P2 z Round to three decimal places as needed Find the p value for this test p value Round to three decimal places as needed What is the conclusion for this test Can we conclude that Drug V causes an increased risk of heart attack OC Ho P1 P2 Ha P1 P2 OF Ho P P2 H P P2 OA No because Ho was not rejected OB Yes because the experiment satisfies the cause and effect relationship conditions and because Ho was rejected OC No because Ho was rejected O D Yes because the experiment satisfies the cause and effect relationship conditions and because Ho was not rejected

Describe the range of values for the correlation coefficient Choose the correct answer below A The range of values for the correlation coefficient is 0 to 1 inclusive OB The range of values for the correlation coefficient is 1 to 1 inclusive OC The range of values for the correlation coefficient is 1 to 1 not inclusive D The range of values for the correlation coefficient is 0 to 1 not inclusive

Identify the explanatory varia and the response variable A farmer wants to determine if the amount of sunlight received by similar crops can be used to predict the harvest of the crop The explanatory variable is the The response variable is the farmer amount of sunlight harvest of the crop

What conditions are necessary in order to use the t test for testing the difference between two population Choose the correct answer below O A The population standard deviations are unknown The populations are normally distributed or each sample size is at least 30 OB The population standard deviations are known The samples are randomly selected and independent The populations are normally distributed or each sample size is at least 30 OC The population standard deviations are unknown The samples are randomly selected and independent The populations are normally distributed or each sample size is at least 30 OD The population standard deviations are unknown The samples are randomly selected and independent

Two variables have a positive linear correlation Does the dependent variable increase or decrease as the independent variable increases What if the variables have a negative linear correlation When two variables have a positive linear correlation does the dependent variable increase or decrease as the independent variable increases O Decrease O Increase When two variables have a negative linear correlation does the dependent variable increase or decrease as the independent variable increases O Decrease O Increase

2 Abiezer and Syed have been talking smack about each other as they prepare to compete head to head in a big bowling tournament The following table shows each of their top 15 scores a Create a double sided stem leaf plot for the data b Determine the CT s range and skew for each of them Abiezer Mean Median Mode Range Skew Abi 56 78 90 92 64 85 79 92 88 97 86 78 89 94 99 Syed 76 87 55 63 81 65 57 73 56 66 75 77 86 93 78 Syed Mean Median Mode Range Skew

Outpatient Satisfaction Likert Score 0 to 5 Dependent Variable Outpatient Satisfaction Likert Score 0 not satisfied to 5 Very Satisfied vs Time minutes with Doctor in Outpatient Clinic Consultation Scatter Plot n 30 Time minutes with Doctor in Outpatient Clinic Consultation Independent Variable 5 Draw a box and whisker plot for the data set 23 26 25 22 21 22 28 23 29 20 Histogram of Stopping Distance 40 15 60 Stopping Distance 80 100 20 120 4 Sarah is working for a clinic that is trying to find a balance between patient satisfaction and the number of patients their doctors can see in a day The result of her work is the graph at the left a Draw a line of best fit b What is the correlation if any between time spent with a patient and their satisfaction If so what type of correlation is it c Determine the equation of the line curve of best fit if there is one d Based on this data what would the expected satisfaction rate if a doctor spends 12 minutes with a patient 6 Clas Median 7 For the histogram at the left determine the estimated Mean Mode Range Skew 3 What is the relationship between independent and dependent variables the following as discrete D or continuous C data a The number of parts damaged during transportation b The amount of rain that falls during a storm c Weight of truck d Shoe size

1 Marcus wants to prove that vanilla ice cream is the best and so polls 100 of his fellow students as to their favorite flavor His results are as follows 15 strawberry 18 vanilla 9 mint chocolate chip 22 moosetracks 7 butter pecan 1 superman 20 chocolate and 8 cookies cream a Should he use a histogram or bar graph to display his data b Create an appropriate labeled graph chart c Is this an example of qualitative or quantitative data d How is qualitative data different from quantitative data