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Chapter 4: Numeric Ways of Describing DataPowerPoint Presentation

Chapter 4: Numeric Ways of Describing Data

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Chapter 4: Numeric Ways of Describing Data

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Chapter 4:Numeric Ways of Describing Data

- Mean
- Formula
- Substitution
- Answer
- Calculator
- Symbols

- Median
- Even, odd sample size

- Using mean vs. median
- Mean for symmetric samples
- Median for skewed samples

- 10% trimmed mean ignores the top 10% and lowest 10% of observations
- Order of resistance to outliers:
- Least resistant:
- Moderately resistant:
- Most resistant:

Mean

Trimmed mean

Median

- Symbols
- Proportion is always between 0 and 1

- Variance, standard deviation
- Symbols
- Formulas
- Substitution
- Calculator
- Units

- Construction
- 5 number summary: Q1, Q3, median, minimum, maximum
- Outliers: <Q1 – 1.5IQR, >Q3 + 1.5IQR

- Interpretation / Comparing
- Center – median
- Shape – cannot tell from boxplot
- Spread – compare whiskers, upper/lower half of box
- When comparing:
- Look for overlap
- Compare whiskers / boxes – which distribution has more variability?

- Used for approximately normal distributions
- If a histogram can be well approximated by a normal curve, then:
- Approximately 68% of the observations are within 1 s.d. of the mean
- 95% 2 s.d.
- 99.7% 3 s.d.

- To compute:

- Interpret:
- Tells number of standard deviations from mean

- Tells proportion/percent of observations at or below that value
- If you score at the 83rd percentile on the ACT, then you scored the same as or better than 83% of students
- If mean is 64 and s.d. is 2, find the score you would need to be at the 90th percentile: