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UK MA 111 - MA 111 Review for Exam 6

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MA 111 Review for Exam 6Exam 6 (given in class on Thursday, December 3) will cover Unit 6: Descriptive Statistics.Use Chapter 14 in the textb ook as a study tool.You should be familiar with the following key ideas:• Understand how to make and/or interpret the following graphical representations of data:– frequency table– bar graph– histogram– pictogram– pie chart• Remember the differences between continuous and discrete variables, and between nu-merical and categorical variables. Understand which of the above graph types are bestsuited for these different types of variables.• Be able to critique a graph. What are some common ways that graphs can be made sothey mislead the viewer?• Know the definition of the mean (or average) and how to calculate it for a given data set.• Know the definition of the pth percentile and how to find it for a data set.• Understand t he meanings of median, first quartile, and third quartile:– The first quartile Q1is the 25th percentile.– The median M is the 50th percentile.– The third quartile Q3is the 75th percentile.• Be able to make and/or interpret a box-and-whisker plot.• Know the definition of the range and the interquartile range.1Practice ProblemsUse the odd exercises on pages 545-554 of the text to supplement these. You can check youranswers in the back of the book.1. Supp ose you are given the following data table:Favorite Colors of a Third G rade Classred 3orange 1yellow 4green 3blue 7purple 2(a) Choose a graphical representatio n and use it to represent the data in the table.(b) Other than the graph you just chose, name another type of graph that wo uld beappropriate for representing this data.(c) Name a type of graph that wo uld be inappropriate for representing this type of data,and explain why.2. Supp ose you want to make a pie chart of the age of students in MA111. If 39% of thestudents are 19 years old, how big would the corresponding slice of the pie be? Calculatethe size of the centr al angle of the slice.3. Consider the following two data sets o f exam scores for two different sections of a course:Class A = {40, 52, 65, 66, 68, 71, 72, 73, 77, 77, 78, 78, 80, 81, 81, 83, 86, 87, 92, 99}Class B = {55, 65, 66, 68, 72, 72, 73, 74, 7 6, 78, 79, 79, 80, 81, 85, 85, 85, 87, 90, 95}(a) Find the median, first quartile Q1and third quartile Q3for each class.(b) The professor wants to recommend the top 10% of each class for a scholarship. Howmany students will she recommend? (Remember, she will recommend students fromeach class).(c) Create box and whisker plots for both classes on a single axis.40 45 50 55 60 65 70 75 80 85 90 95 10024. Mike’s average on the first five exams is 88. What must he earn on the next exam to raisehis exam average to 90?5. A professor is teaching two sections of MA111. Section 1 has 35 students, and Section2 has 28 students. On the last exam, the average score fo r Section 1 was 73, while theaverage score for Section 2 was 78.For all of the students combined, find the average score for the exam.6. Look at the hand-out of graphs I distributed at the beginning of this unit. Be able toidentify the ways that each graph is misleading, and suggest a way to improve the graphs.7. Consider the following data set:{7, 59, 25, 2 7, 64 , 70, 68, 11, 45, 5, 1 7 , 45, 52, 21, 26}(a) Find the 30th percentile of the data set.(b) Find the 60th percentile of the da ta set.(c) Find the 95th percentile of the data set.(d) Find the 50th percentile of the da ta set.8. Consider the data set {2, 18, 19, 22, 24, 24, 25, 78}.(a) Find the range.(b) Find the interquartile range.(c) Why might we consider the interquartile r ange a better measure of the spread of thisparticular set?9. Give an example of a data set with N = 5 with the median less than the mean.10. Try questions 45 and 46 on pages 549-550 of the textbook. Be able to interpret box-and-whisker plots to answer similar questions.Question 46 has two typos. The question should read:(a) Fill in the blank: Of the 612 engineering graduates, at most had a startingsalary g reater than $45,000.(b) Fill in the blank: If there were 240 agriculture graduates with starting salaries o f$35,000 or less, the total number of agriculture graduates is approximately .11. In 200 6, the median SAT score was d756,155, where {d1, d2, . . . , dN} denotes the dat a setof all SAT scores ordered from lowest to highest. Determine the number of students Nwho took the SAT in


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