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Chapter 4: Numeric Ways of Describing Data - PowerPoint PPT Presentation

Chapter 4: Numeric Ways of Describing Data. Measures of Center. Mean Formula Substitution Answer Calculator Symbols Median Even, odd sample size Using mean vs. median Mean for symmetric samples Median for skewed samples. Trimmed Mean.

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Chapter 4:Numeric Ways of Describing Data

• Mean

• Formula

• Substitution

• 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?

Boxplot Example

• 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.

z – score

• 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: