MA 111 Review for Exam 6 Solutions Exam 6 given in class on Thursday December 3 will cover Unit 6 Descriptive Statistics Use Chapter 14 in the textbook 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 numerical and categorical variables Understand which of the above graph types are best suited for these different types of variables Be able to critique a graph What are some common ways that graphs can be made so they 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 the meanings of median first quartile and third quartile The first quartile Q1 is the 25th percentile The median M is the 50th percentile The third quartile Q3 is 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 1 Practice Problems Use the odd exercises on pages 545 554 of the text to supplement these You can check your answers in the back of the book 1 Suppose you are given the following data table Favorite Colors of a Third Grade Class red 3 orange 1 yellow 4 green 3 blue 7 purple 2 a Choose a graphical representation and use it to represent the data in the table You could make a bar graph or a pie chart A pictogram might also work maybe with crayons making up the bars of the bar graph Here s the bar graph b Other than the graph you just chose name another type of graph that would be appropriate for representing this data As above a bar graph pie chart or pictogram is appropriate c Name a type of graph that would be inappropriate for representing this type of data and explain why A histogram would be inappropriate because the variable is not numerical and continuous Remember that histograms are best for continuous variables like height weight etc 2 Suppose you want to make a pie chart of the age of students in MA111 If 39 of the students are 19 years old how big would the corresponding slice of the pie be Calculate the size of the central angle of the slice The central angle would be 39 3 6 140 4 2 3 Consider the following two data sets of exam scores for two different sections of a course Class A Class B 40 52 65 66 68 71 72 73 77 77 78 78 80 81 81 83 86 87 92 99 55 65 66 68 72 72 73 74 76 78 79 79 80 81 85 85 85 87 90 95 a Find the median first quartile Q1 and third quartile Q3 for each class Both classes have N 20 students Notice the lists are already sorted Class A The median is the average of the 10th and 11th values M 77 5 The locator for Q1 is L 25 20 5 So Q1 is the average of the 5th and 6th values Q1 69 5 The locator for Q3 is L 75 20 15 So Q3 is the average of the 15th and 16th values Q3 82 For Class B the locators are all the same because N is the same So M 78 5 Q1 72 and Q3 85 b The professor wants to recommend the top 10 of each class for a scholarship How many students will she recommend Remember she will recommend students from each class The top 10 of each class is found by computing the 90th percentile So L 9 20 18 The 90th percentile is the average of the 18th and 19th values of each class So there are two students in Class A they got a 92 and a 99 and two students in Class B they got a 90 and a 95 Overall the professor will recommend 4 students c Create box and whisker plots for both classes on a single axis 40 45 50 55 60 65 70 75 80 85 90 95 100 4 Mike s average on the first five exams is 88 What must he earn on the next exam to raise his exam average to 90 Since the first five exams averaged to be 88 the sum of all of those five exam scores was 88 5 440 3 Let the next exam grade be g Then Mike wants 440 g 6 440 g 440 g g g 90 90 6 540 540 440 100 5 A professor is teaching two sections of MA111 Section 1 has 35 students and Section 2 has 28 students On the last exam the average score for Section 1 was 73 while the average score for Section 2 was 78 For all of the students combined find the average score for the exam The sum of scores in Section 1 was 73 35 2555 The sum of scores in Section 2 was 78 28 2184 So the average of all the scores is 2555 2184 4739 75 2 35 28 63 6 Look at the hand out of graphs I distributed at the beginning of this unit Be able to identify the ways that each graph is misleading and suggest a way to improve the graphs Some of the ways graphs are misleading include altering the vertical axis especially cutting it off before 0 in order to make a graph appear more dramatic than it actually is using items in a pictograph that actually change by volume or area not height The heights may be correct but the resulting change in volume or area appears more dramatic not labeling or mislabeling axes If you have any questions about a specific example please ask 7 Consider the following data set 7 59 25 27 64 70 68 11 45 5 17 45 52 21 26 a Find the 30th percentile of the data set We first need to sort the data 5 7 11 17 21 25 26 27 45 45 52 59 64 68 70 4 Notice N 15 items in the list So L 3 15 4 5 We round this up to 5 The 30th percentile is 21 b Find the 60th percentile of the data set L 6 15 9 We take the average of the 9th and 10th values The 60th percentile is 48 5 c Find the 95th percentile of the data set L 95 15 14 25 We round up to 15 The 95th percentile is 70 d Find the 50th percentile of the data set This will be the median Since N is odd we take the middle value 27 8 Consider the data set 2 18 19 22 24 24 25 78 a Find the range 78 2 76 b Find the interquartile range We first have to find Q1 and Q3 There are N 8 …