Chapter 2 (Intro and 2.1) GLN

Chapter 2 – Organizing and Summarizing Data OUTLINE 2.1 Organizing Qualitative Data 2.2 Organizing Quantitative Data: The Popular Displays 2.3 Additional Displays of Quantitative Data 2.4 Graphical Misrepresentations of Data Putting It Together Chapter 1 discussed how to identify the research objective and collect data. We learned that data can be obtained from either observational studies or designed experiments. When data are obtained, they are referred to as raw data . The purpose of this chapter is to learn how to organize raw data into a meaningful form so that we can understand what the data are telling us. The first step in determining how to organize raw data is to determine whether the data is qualitative or quantitative.

Section 2.1 Organizing Qualitative Data Objectives  Organize Qualitative Data in Tables  Construct Bar Graphs  Construct Pie Charts Objective 1: Organize Qualitative Data in Tables O BJECTIVE 1, P AGE 1 1) What is used to list each category of data and the number of occurrences for each category of data? A frequency distribution lists each category of data the number of occurrences for eachcatagory of data. O BJECTIVE 1, P AGE 2 Example 1 Organizing Qualitative Data into a Frequency Distribution A physical therapist wants to determine types of rehabilitation required by her patients. To do so, she obtains a simple random sample of 30 of her patients and records the body part requiring rehabilitation. (See Table 1.) Construct a frequency distribution of location of injury. Table 1 Back Back Hand Wrist Back Back Groin Elbow Back Back Back Groin Shoulder Shoulder Hip Knee Hip Shoulder Neck Knee Knee Shoulder Shoulder Neck Back Back Back Back Knee Back Data from Krystal Catton, student at Joliet Junior College Back IIIIIIIIIIII12 Hand II 2 Wrist II 2 Groin I 1 Elbow I 1 Shoulder IIII 4 Hip II 2 Knee IIIII 5 Neck I 1 O BJECTIVE 1, P AGE 3 2) In any frequency distribution, it is a good idea to add up the frequency column. What should the total be equal to? Spring 2024

O BJECTIVE 1, P AGE 8 5) When working with a relative frequency distribution, what should the total of the relative frequencies be equal to? Why? The sum should equal 1. Objective 2: Construct Bar Graphs O BJECTIVE 2, P AGE 1 6) Explain how a bar graph is constructed. What do the heights of each rectangle represent? A bar graph is cunstructed by labeling each category of data on either the horizontal or vertical axis andthe frequency of the category on the other axis. Rectangles of equal width are drawn for each categorythe height of each rectangle represents the category's frequency or relative frequency. O BJECTIVE 2, P AGE 2 Example 3 Constructing a Frequency and Relative Frequency Bar Graph Use the data summarized in Table 3 to construct a frequency bar graph and relative frequency bar graph. Table 3 Relative Body Part Frequency Frequency Back 12 0.4 Hand 2 0.0667 Wrist 2 0.0667 Groin 1 0.0333 Elbow 1 0.0333 Shoulder 4 0.1333 Hip 2 0.0667 Knee 5 0.1667 Neck 1 0.0333 Spring 2024

O BJECTIVE 2, P AGE 4 7) What is a Pareto chart? A pareto chart is a bar graph whose bars are drawn in decreasing order of frequency or relative frequency. O BJECTIVE 2, P AGE 5 8) Explain why it is best to use relative frequencies when comparing data sets. It is best to use relative frequencys because different sample or population sizes makecomparision using frequencies difficult or misleading. O BJECTIVE 2, P AGE 6 Example 4 Comparing Two Data Sets The frequency data in Table 4 represent the educational attainment (level of education) in 1990 and 2016 of adults 25 years and older who are U.S. residents. The data are in thousands. So 39,344 represents 39,344,000. Table 4 Educational Attainment 1990 2016 Not a high school graduate 39,344 23,453 High school diploma 47,643 62,002 Some college, no degree 29,780 36,003 Associate's degree 9792 21,657 Bachelor's degree 20,833 44,778 Graduate or professional degree 11,478 27,122 Totals 158,870 215,015 A) Draw a side-by-side relative frequency bar graph of the data.

O BJECTIVE 3, P AGE 2 Example 5 Constructing a Pie Chart The frequency data presented in Table 6 represent the educational attainment of U.S. residents 25 years and older in 2016. The data are in thousands so 23,453 represents 23,453,000. Construct a pie chart of the data. Table 6 Educational Attainment 2016 Not a high school graduate 23,453 High school diploma 62,002 Some college, no degree 36,003 Associate's degree 21,657 Bachelor's degree 44,778 Graduate or professional degree 27,122 Totals 215,015 O BJECTIVE 3, P AGE 5 Answer the following after watching the video. 11) Which graph, a pie chart or a bar graph, is better at comparing one category to another category? Bar graph 12) Which graph, a pie chart or a bar graph, is better at comparing one category to the whole? Pie chart