68 CHAPTER 2 Descriptive Statistics The median of a data set is the value that lies in the middle of the data when the data set is ordered. The median measures the center of an ordered data set by dividing it into two equal parts. When the data set has an odd number of entries, the median is the middle data entry. When the data set has an even number of entries, the median is the mean of the two middle data entries. DEFINITION Finding the Median Find the median of the weights listed in Example 1. SOLUTION To find the median weight, first order the data. 223 235 235 268 274 285 290 Because there are seven entries (an odd number), the median is the middle, or fourth, entry. So, the median weight is 268 pounds. TRY IT YOURSELF 2 Find the median of the points scored by the 55 winning teams listed on page 39. Answer: Page A36 In a data set, the number of data entries above the median is the same as the number below the median. For instance, in Example 2, three of the weights are below 268 pounds and three are above 268 pounds. Finding the Median In Example 2, the adult weighing 285 pounds decides to not participate in the study. What is the median weight of the remaining adults? SOLUTION The remaining weights, in order, are 223 235 235 268 274 290. Because there are six entries (an even number), the median is the mean of the two middle entries. Median = 235 + 268 2 = 251.5 So, the median weight of the remaining adults is 251.5 pounds. You can check your answer using technology, as shown below using Excel. EXCEL 251.5 A 1 2 B C D E F 223 235 235 268 274 290 =MEDIAN(A1:F1) TRY IT YOURSELF 3 The points scored by the winning teams in the Super Bowls for the National Football League’s 2005 through 2020 seasons are listed. Find the median. 21 29 17 27 31 31 21 34 43 28 24 34 41 13 31 31 Answer: Page A36 EXAMPLE 2 EXAMPLE 3 Tech Tip You can use technology such as Minitab, Excel, StatCrunch, or the TI-84 Plus to find the mean and median of a data set. For instance, to find the mean and median of the weights listed in Example 1 on a TI-84 Plus, enter the data in L1. Next, press 2nd LIST and from the MATH menu choose mean. Then press 2nd LIST and from the MATH menu choose median. TI-84 PLUS mean(L1) median(L1) 258.5714286 268
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