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Unit 4, Day 3

Unit 4, Day 3. SWBAT determine the best measure of central tendency to represent a set of data. Vocabulary. CENTRAL TENDENCY : describes/summarizes the center of a data set. Mean, median, mode OUTLIER: something that is very different from everything else $0.05, $123.00, $124.00, $130.00.

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Unit 4, Day 3

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  1. Unit 4, Day 3 SWBAT determine the best measure of central tendency to represent a set of data

  2. Vocabulary • CENTRAL TENDENCY: describes/summarizes the center of a data set. • Mean, median, mode • OUTLIER: something that is very different from everything else $0.05, $123.00, $124.00, $130.00

  3. Determining best measureRULes We are looking for a measure(s) that is close to MOST of the data • Check for a mode, if there is NOT a mode, it cannot be a good measure • Eliminate “mode” as a possible answer • If the mode is an outlier, it is not a good measure • 1, 1, 68, 69, 70, 74 • Eliminate “mode” as a possible answer

  4. Determining best measureRULes • Examine the data for outliers. If there are outliers in only one direction, the mean will not be a good measure. • 1, 100, 105, 110, 110, 111 • 1, 100, 105, 110, 110, 111, 2000 • If these rules do not apply, then any measure of central tendency can be used to represent the data

  5. 4, 5, 6, 7, 8, 98 • The mode • The mean • The mode and the median • The median Mean actually is about 121… so you can see that’s not the best measure Order numbers Is there a mode? No, eliminate Are there outliers? Yes, eliminate mean

  6. Is there a mode? No – eliminate it • Is there an outlier? Yes, football coaches make a lot more money • In one or two directions? One – eliminate mean

  7. What measure(s) Best represents the salaries of most people? • The median is the only measure that represents most salaries. There is no mode, and the outlier causes the mean not to be representative

  8. 2. 75, 80, 85, 90 • Order the numbers first • Rule 1: No mode – eliminate (A and C) • Rule 2: There is no mode, so it is not an outlier • Rule 3: No outliers • Best choice is D.

  9. 3. 3, 16, 17, 17, 18, 18 • Order the numbers first • Rule 1: Yes, mode is 18 • Rule 2: The mode is not an outlier • Rule 3: Three is an outlier, eliminate mean • I chose median and mode. I eliminated mean because there is an outlier of 3.

  10. Independent Practice • Put all of the sets in order from least to greatest • If there’s a mode, identify it • If there’s an outlier, identify it.

  11. Independent practice review • D. • No mode, and there’s an outlier (not mean) • D. • No mode, and no outliers (keep mean) • D. • Mode is 7, no outliers (keep mean) • Mode, mean, median all work • Mode is not an outlier, no other outliers • Mean, and median • No mode, and no outliers

  12. Independent practice review • Mean is NOT good because 1000 is an outlier • A • Possibly D because the 20 isn’t quite far enough away to be a real outlier • B. the mean is NOT a good measure because 5 is an outlier • All measures of central tendency work, there is a mode and there are no outliers • Mean and median are best, but you could also include mode because it’s not an outlier

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