Business Statistics 1-1 Chapter Two Describing Data: Frequency Distributions and Graphic Presentation GOALS When you have completed this chapter, you will be able to: ONE Organize data into a frequency distribution. TWO Portray a frequency distribution in a histogram, frequency polygon, and cumulative frequency polygon. THREE Develop a stem-and-leaf display. FOUR Present data using such graphic techniques as line charts, bar charts, and pie charts.

Business Statistics Frequency Distribution Frequency distribution: A grouping of data into mutually exclusive categories showing the number of observations in each category. 2-2

Business Statistics Construction of a Frequency Distribution 2-3

Business Statistics Frequency Distribution Class mark (midpoint): A point that divides a class into two equal parts. This is the average between the upper and lower class limits. Class interval: For a frequency distribution having classes of the same size, the class interval is obtained by subtracting the lower limit of a class from the lower limit of the next class. 2-4

Business Statistics EXAMPLE 1 Dr. Tillman is the dean of the school of business and wishes to determine the amount of studying business school students do. He selects a random sample of 30 students and determines the number of hours each student studies per week: 15.0, 23.7, 19.7, 15.4, 18.3, 23.0, 14.2, 20.8, 13.5, 20.7, 17.4, 18.6, 12.9, 20.3, 13.7, 21.4, 18.3, 29.8, 17.1, 18.9, 10.3, 26.1, 15.7, 14.0, 17.8, 33.8, 23.2, 12.9, 27.1, Organize the data into a frequency distribution. 2-5

Business Statistics EXAMPLE 1 continued 2-6 Consider the first two classes. The class marks are 10 and 15. The class interval is 5 ( ).

Business Statistics Relative Frequency Distribution The relative frequency of a class is obtained by dividing the class frequency by the total frequency. 2-7

Business Statistics Stem-and-Leaf Displays Stem-and-Leaf Display: A statistical technique for displaying a set of data. Each numerical value is divided into two parts: the leading digits become the stem and the trailing digits the leaf. Note: An advantage of the stem-and-leaf display over a frequency distribution is we do not lose the identity of each observation. 2-8

Business Statistics EXAMPLE 2 Colin achieved the following scores on his twelve accounting quizzes this semester: 86, 79, 92, 84, 69, 88, 91, 83, 96, 78, 82, 85. Construct a stem-and-leaf chart for the data. 2-9

Business Statistics Graphic Presentation of a Frequency Distribution The three commonly used graphic forms are histograms, frequency polygons, and a cumulative frequency distribution (ogive). Histogram: A graph in which the classes are marked on the horizontal axis and the class frequencies on the vertical axis. The class frequencies are represented by the heights of the bars and the bars are drawn adjacent to each other. 2-10

Business Statistics Graphic Presentation of a Frequency Distribution A frequency polygon consists of line segments connecting the points formed by the class midpoint and the class frequency. A cumulative frequency distribution (ogive) is used to determine how many or what proportion of the data values are below or above a certain value. 2-11

Business Statistics Histogram for Hours Spent Studying 2-12

Business Statistics Frequency Polygon for Hours Spent Studying 2-13

Business Statistics Less Than Cumulative Frequency Distribution For Hours Studying 2-14

Business Statistics Bar Chart A bar chart can be used to depict any of the levels of measurement (nominal, ordinal, interval, or ratio). EXAMPLE 3: Construct a bar chart for the number of unemployed people per 100,000 population for selected cities of

Business Statistics EXAMPLE 3 continued 2-16

Business Statistics Bar Chart for the Unemployment Data 2-17

Business Statistics Pie Chart A pie chart is especially useful in displaying a relative frequency distribution. A circle is divided proportionally to the relative frequency and portions of the circle are allocated for the different groups. EXAMPLE 4: A sample of 200 runners were asked to indicate their favorite type of running shoe. 2-18

Business Statistics EXAMPLE 4 continued Draw a pie chart based on the following information. 2-19

Business Statistics Pie Chart for Running Shoes 2-20