SECTION 2.3 Measures of Central Tendency 69 The mode of a data set is the data entry that occurs with the greatest frequency. A data set can have one mode, more than one mode, or no mode. When no entry is repeated, the data set has no mode. When two entries occur with the same greatest frequency, each entry is a mode and the data set is called bimodal. DEFINITION Finding the Mode Find the mode of the weights listed in Example 1. SOLUTION To find the mode, first order the data. 223 235 235 268 274 285 290 From the ordered data, you can see that the entry 235 occurs twice, whereas the other data entries occur only once. So, the mode of the weights is 235 pounds. TRY IT YOURSELF 4 Find the mode of the points scored by the 55 winning teams listed on page 39. Answer: Page A36 Finding the Mode At a political debate, a sample of audience members was asked to name the political party to which they belonged. Their responses are shown in the table. What is the mode of the responses? Political party Frequency, f Democrat 46 Republican 34 Independent 39 Other/don’t know 5 SOLUTION The response occurring with the greatest frequency is Democrat. So, the mode is Democrat. Interpretation In this sample, there were more Democrats than people of any other single affiliation. TRY IT YOURSELF 5 In a survey, 12,648 adults were asked, “How much confidence, if any, do you have in elected officials to act in the best interests of the public?” Of those surveyed, 531 said “a great deal,” 4073 said “a fair amount,” 5970 said “not too much,” 1922 said “none at all,” and 152 did not provide an answer. What is the mode of the responses? (Adapted from Pew Research Center) Answer: Page A36 The mode is the only measure of central tendency that can be used to describe data at the nominal level of measurement. But when working with quantitative data, the mode is rarely used. EXAMPLE 4 EXAMPLE 5
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