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Lesson 1.6 %u2022 Measuring Center 63DEFINITION ResistantA statistical measure is resistant if it is not affected much by extreme data values.The median is a resistant measure of center. In the preceding example, the median travel time to school for the sample of 20 high school students is 11.5 minutes. If we remove the possible outlier who travels 70 minutes to get to school, the median travel time to school for the remaining 19 students is nearly the same: 11 minutes.The activity gives a physical interpretation of the mean as the balance point of a distribution. For the data on travel time to school for a random sample of 20 U.S. high school students, the dotplot balances at x = 17 minutes.25 30 605550454035Travel time to school (min)0 5 10 15 20 65 70Comparing the Mean and the MedianWhich measure%u2014the mean or the median%u2014should we report as the center of a distribution? That depends on both the shape of the distribution and whether there are any outliers.Shape: Figure 1.9 shows the mean and median for dotplots with three different shapes. Notice how these two measures of center compare in each case. The mean is pulled in the direction of the long tail in a skewed distribution.Interpreting the meanIn this activity, you will investigate a physical interpretation of the mean of a distribution.1. Stack 5 pennies at the 6-inch mark on a 12-inch ruler. Place a pencil under the ruler to make a %u201cseesaw%u201d on a desk or table. Move the pencil until the ruler balances. What is the relationship between the location of the pencil and the mean of the five data values: 6, 6, 6, 6, and 6?2. Move one penny off the stack to the 8-inch mark on your ruler. Now move one other penny so that the ruler balances again without moving the pencil. Where did you put the other penny? What is the mean of the five data values represented by the pennies now?3. Move one more penny off the stack to the 2-inch mark on your ruler. Now move both remaining pennies from the 6-inch mark so that the ruler still balances with the pencil in the same location. Is the mean of the data values still 6?4. Discuss with your classmates: Why is the mean called the %u201cbalance point%u201d of a distribution?AC TIVIT Y Ann Heath%u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.