Sec 2.1

Section 2.1: Relative Frequency Page 1 Definition 1. A histogram is constructed by drawing rectangles for each class of data. The height of each rectangle is the frequency or relative frequency of the class. The width of each rectangle is the same and the rectangles touch each other. In summarizing quantitative data, first determine whether the data are discrete or continu- ous. If the data are discrete with relatively few different values of the variable, then the categories of data (called classes) will be the observations (as in qualitative data). If the data are discrete, but with many different values of the variable or if the data are continuous, then categories of data (the classes) must be created using intervals of numbers. To make one, first decide on the interval size (width). This may change for every dataset. Example 1 (Car Batteries) . The following data specifies the “life” of 40 similar car batteries recorded to the nearest tenth of a year. The batteries are guaranteed to last 3 years. (Data from pg 21 of our textbook.) 1.6 2.6 3.1 3.2 3.4 3.7 3.9 4.3 1.9 2.9 3.1 3.3 3.4 3.7 3.9 4.4 2.2 3.0 3.1 3.3 3.5 3.7 4.1 4.5 2.5 3.0 3.2 3.3 3.5 3.8 4.1 4.7 2.6 3.1 3.2 3.4 3.6 3.8 4.2 4.7 Draw a histogram for this dataset starting at 1.5 and using widths of 0.5.

Section 2.1: Relative Frequency Page 2 blank

Section 2.1: Relative Frequency Page 4 Are there any unusual features? Definition 2 (Outliers) . Points that are far away from the rest of the points. Example 2 . The following frequency distribution represents the sprint speed (in feet per second) of all players in Major League Baseball during the 2018 baseball season. Answer the following questions: 1. Find the number of classes 2. Find the class width. 3. What percentage of players had a sprint speed between 24 and 25.9 ft/sec? 4. What percentage of players had a sprint speed less than 24 ft/sec?

Section 2.1: Relative Frequency Page 5 Example 3 . A researcher with A. C. Nielsen wanted to determine the number of televisions in households. He conducts a survey of 20 randomly selected households and obtains the following data. 0 1 2 3 1 2 1 3 1 1 1 3 2 2 4 2 3 4 1 5 1. Are these data discrete or continuous? 2. Construct a frequency distribution of the data. 3. Construct a relative frequency distribution of the data. televisions? 4. What percentage of households in the survey have four or more televisions? 5. Construct a frequency histogram of the data. 6. Construct a relative frequency histogram of the data. 7. Describe the shape of the distribution.