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Determining the Best Measure of Central Tendency for Data Representation

In this lesson, students will learn to determine the most appropriate measure of central tendency—mean, median, or mode—when analyzing a data set. Key concepts such as central tendency, outliers, and rules for identifying the best measure will be discussed. Students will practice ordering data, identifying modes and outliers, and applying elimination rules to conclude which measure best represents the data. By engaging in independent practice, students will enhance their understanding of how outliers affect mean and median values.

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Determining the Best Measure of Central Tendency for Data Representation

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Presentation Transcript

  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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