MFT TP O Range and Outliers CA Standards SDAP 1.1 SDAP 1.3 Goal: Analyze how the inclusion or exclusion of outliers affects measures of central tendency. Vocabulary Lower extreme: The least data value in a data set Upper extreme: The greatest data value in a data set Lower quartile: The median of the lower half of the data Upper quartile: The median of the upper half of the data Range: The difference between the upper and lower extremes of a data set Interquartile range: The difference between the upper and lower quartiles Outlier: A value in a data set that is much greater or much less than the other values Box-and-whisker plot: A data display that divides data values into four parts Copyright © by McDougal Littell, a division of Houghton Mifflin Company. Lesson 7.4 • Course 1 Notetaking Guide 153 EXAMPLE 1 Computing Statistics Find the median, extremes, quartiles, range, and interquartile range of the data set 22, 36, 24, 40, 18, 56, 33, 87, and 25. Step 1 Order the data and identify the median and the extremes. 18 22 24 25 Lower extreme 40 56 87 Upper extreme Step 2 Identify the quartiles using the lower and upper halves of the data. 18 22 24 25 36 Lower quartile 40 56 If a data set has an odd number of values, the median is not included in either the lower half or upper half. 36 Median WATCH OUT! 33 87 Upper quartile 22 24 2 23 40 56 2 48 Step 3 Subtract the extremes to find the range: 87 18 69 . Step 4 Subtract the quartiles to find the interquartile: range: 48 23 25 . EXAMPLE 2 Describing Effects of Outliers Use the data set 59, 60, 64, 66, 68, 72, and 115. The data value 115 is an outlier. How does the exclusion of the outlier affect the mean? Explain. Solution Calculate the mean of the original data set. Mean: 504 72 } 59 + 60 + 64 + 66 + 68 + 72 + 115 }}} 7 7 Then calculate the mean excluding the outlier 115 . Mean: 59 + 60 + 64 + 66 + 68 + 72 6 }}} 389 64.8 } 6 The mean decreases by about 7.2 . The mean decreases because the outlier is the greatest data value . 154 Lesson 7.4 • Course 1 Notetaking Guide Copyright © by McDougal Littell, a division of Houghton Mifflin Company. Guided Practice Use the data set 14, 12, 18, 15, 13, and 4. 1. Find the median, extremes, quartiles, range, interquartile range, and any outliers of the data set. Median: 13.5; lower extreme: 4, upper extreme: 18; lower quartile: 12; upper quartile: 15; range: 14; interquartile range: 3; outlier: 4 3 EXAMPLE Using a Box-and-Whisker Plot Test Scores The box-and-whisker plots below show the spread of the differences between the prices of winter coats at 25 stores in a mall. The data in the first plot have an outlier of $29. The second plot displays the same data but does not include the outlier. How does excluding the outlier affect the median and the range of the data? 20 30 29 Lower extreme 40 50 60 80 90 100 66 75 87 95 Median Lower Upper Upper quartile quartile extreme 56 Lower extreme Homework 70 68 75 87 95 Upper Lower Median Upper extreme quartile quartile Solution When the outlier is included , the median is 75 and the range is 66 . When the outlier is excluded , the median is 75 and the range is 39 . The median does not change and the range greatly decreases when the outlier is excluded. Copyright © by McDougal Littell, a division of Houghton Mifflin Company. Lesson 7.4 • Course 1 Notetaking Guide 155
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