# 3.4 Measures of Position - PowerPoint PPT Presentation

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3.4 Measures of Position. Objectives: By the end of this section, I will be able to… Find percentiles for both small and large data sets. Calculate z -scores, and explain why we use them. Use z -scores to detect outliers.

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3.4 Measures of Position

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### 3.4 Measures of Position

Objectives:

By the end of this section, I will be

able to…

• Find percentiles for both small and large data sets.

• Calculate z-scores, and explain why we use them.

• Use z-scores to detect outliers.

## 20. What sport used the term home run before baseball? Lacrosse or Cricket.

• HOW MANY DID YOU GET RIGHT?

18

42

T

T

29

2

1903

Thanksgiving

1

Muhammed

Old Joe

\$35

Skin

Light

Cali

Onion

Pepper

Garth Brooks

## 20. What sport used the term home run before baseball? Lacrosse or Cricket.

Cricket

### Comparing Scores

• Standardized Tests: SATs, TerraNovas, CTBS, ACTs

• Two ways to compare scores:

• Percentile Rank

• Z-scores

### PERCENTILE RANK

# of Equal scores

Scores that came BEFORE

• B =# of scores that came BEFORE “your” score

• E =#of scores that are the same as “your” score

• N = Total #of people taking the test

Total Number

### PERCENTILE RANK

# of Equal scores

Scores that came BEFORE

Total Number

### z-scores

• Numerical values that are used to compare scores

• It indicates how many standard deviations a data value is from the mean.

### z-scores

MEAN

• Let’s find the meanfirst.

• Now find the standard deviation.

Standard Deviation

USE DECIMALS

FOR z-scores.

• We want them to be as accurate as possible!

+ z-score

means you are ABOVE the

-z-score

means you are BELOW the

0 z-score

means you are the exactly

### Finding an actual score

• If the average senior at UD can drink 9 beers before he/she gets sick with a standard deviation of 1.76, find the amount that the following people actually drank.

Timmy Joe who had a z-score of 5.1

Betty Sue who had a z-score of -0.957

17.976

7.316

### z-scores and OUTLIERS

• If you are between -2 and 2 it is NOT unusual.

• If you are <-3 or >3 it is very unusual and it is an OUTLIER