94 Chapter 3 Numerical Summaries of Data Solution The mean and median height are meaningful, because heights are measurements. The mean and median uniform numbers are not meaningful, because these numbers are just labels. They don’t measure or count anything. Objective 4 Find the mode of a data set The Mode In Section 2.2, we defined a mode to be the highest point of a histogram. There is another definition of this term. The mode of a data set is the value that appears most frequently. EXAMPLE 3.7 Finding the mode Ten students were asked how many siblings they had. The results, arranged in order, were 0 1 1 1 1 2 2 3 3 6 Find the mode of this data set. Explain It Again The mode isn’t really a measure of center: The mode is sometimes classified as a measure of center. However, this isn’t really accurate. The mode can be the largest value in a data set, or the smallest, or anywhere in between. Solution The value that appears most frequently is 1. Therefore, the mode of this data set is 1. When two or more values are tied for the most frequent, they are all considered to be modes. If no value appears more than once, we say that the data set has no mode. SUMMARY • The mode of a data set is the value that appears most frequently. • If two or more values are tied for the most frequent, they are all considered to be modes. • If no value appears more than once, we say that the data set has no mode. Computing the mode for qualitative data The mean and median can be computed only for quantitative data. The mode, on the other hand, can be computed for qualitative data as well. For qualitative data, the mode is the most frequently appearing category. EXAMPLE 3.8 Finding the mode for qualitative data Following is a list of the makes of all the cars rented by an automobile rental company on a particular day. Which make of car is the mode? Honda Toyota Toyota Honda Ford Chevrolet Nissan Ford Chevrolet Chevrolet Honda Dodge Ford Ford Toyota Chevrolet Toyota Toyota Toyota Nissan Solution The most frequent category is “Toyota,” which appears six times. Therefore, the mode is “Toyota.” Check Your Understanding 6. Find the mode or modes, if they exist: a. The sample is 3, 6, 0, 1, 1, 8, 0, 1, 1. b. The sample is 4, 7, 4, 1, 6, 5, 6. c. The sample is 4, 8, 5, 9, 6, 3. Answers are on page 104.
navidi_monk_essential_statistics_1e_ch1_3
To see the actual publication please follow the link above