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Data With Outliers

Data With Outliers. Lesson 3-2 Pg. # 91-93. CA Content Standards. Statistics, Data Analysis, and Probability 1.3: I understand how leaving out or including outliers affects measures of central tendency. Statistics, Data Analysis, and Probability 1.2:

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Data With Outliers

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  1. Data With Outliers Lesson 3-2 Pg. # 91-93

  2. CA Content Standards • Statistics, Data Analysis, and Probability 1.3: I understand how leaving out or including outliers affects measures of central tendency. • Statistics, Data Analysis, and Probability 1.2: I understand how additional data may affect computations of central tendency. • Mathematical Reasoning 2.2: I apply strategies from simpler problems to more difficult problems.

  3. Review Vocabulary: MEASURES OF CENTRAL TENDENCY • Measuring tools (such as mean, median, and mode) that indicate what is typical, or common, in a set of data.

  4. Vocabulary: OUTLIER • An extreme value in a data set, separated from most of the other values.

  5. Objective • Compute the mean, median, mode, and range of data sets with and without outliers to determine how they affect central tendencies. • Math Link: You know how to find the mean, median, and mode of a data set. Now you will learn how one unusual number in a set of data can affect these measures of central tendency.

  6. Example 1. • Miss Flores asked some of her 6th grade math students how many hours of television they watch daily. • Use the data in the table to calculate mean, median, and mode. These calculations will let us know how many hours are most typical per person.

  7. Mean: 1 + 2 + 1 + 1 + 3 + 1 + 2 = 11 = 1.6 7 7 • Median: 1 1 1 1 2 2 3 • Mode: The number 1 appears the most times. 1 is the mode. According to our calculations, most participants watch approximately 1 hour of television every day. ***Note: Even though we have a mean of 1.6, no participant watched exactly 1 and six-tenths of an hour of TV. This is an example of how a mean can describe the group but not any individual member of the group.

  8. Example 2. • Hannah is not listed in the table. She watches 9 hours every day. (Talk about a COUCH POTATO!) Add Hannah’s data to the data set and recalculate the mean, median, and mode. Are the mean, median, and mode affected by this extra data?

  9. Mean: 1 + 2 + 1 + 1 + 3 + 1 + 2 + 9 = 20 = 2.5 8 8 • Median: 1 1 1 1 2 2 3 9 Median = 1.5 • Mode: The number 1 appears the most times. 1 is the mode. According to our calculations, most participants watch between 1 and 2.5 of television every day. Did our mean change when we added Hannah’s information? How about the median? The mode? Would the median or mode change if Hannah watched 4 hours daily? 12 hours?

  10. Hannah’s data is an outlier. An outlier is a number in a data set that is very different from the rest of the numbers. Outliers can have a great effect on the mean. • Outliers usually do not impact the median or mode. • Data sets can have more than one outlier.

  11. Example 3. • Throughout most of the year, Acapulco is very sunny. If you look at the # of wet days from February through May, you see the range is from 0 to 2. But when the rainy season begins in June, the number of wet days jumps to 12. 12 is an outlier in this set of data because it is very different from the rest of the numbers.

  12. The outlier did not affect the mode, and it changed the median slightly. But look what happens to the mean when the June number is included in the data. The mean becomes 3 wet days, which is the same as Feb through May combined.

  13. Identify the outlier. Then find the mean, median, and mode of the data with and without the outlier. 190 210 160 250 1400 190

  14. The Moral of the Story: • An outlier is a value within a set of data that is far below or far above most of the other data. It can affect the median, but usually has the greatest effect on the mean of a set of data.

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