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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

Unit 4, Day 3

SWBAT determine the best measure of central tendency to represent a set of data


Vocabulary
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


Determining best measure rules
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


Determining best measure rules1
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


4 5 6 7 8 98
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


Unit 4 day 3

  • 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


What measure s best represents the salaries of most people
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


2 75 80 85 90
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.


3 3 16 17 17 18 18
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.


Independent practice
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.


Independent practice review
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


Independent practice review1
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