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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

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 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

- 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

- 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?

- 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

- 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

- 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

- 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

- 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 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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