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Chapter 3.3-3.5

MATH 10041 Chapter Notes - Chapter 3.3-3.5: QuartilePremium

by OneClass2511532

1 pages23 viewsSpring 2019

School

Kent State University

Department

Mathematics

Course Code

MATH 10041

Professor

Beverly M Reed

Chapter

3.3-3.5

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3.3: Summaries for Skewed Distributions

Median: the value that would be right in the middle if you were to sort the data from smallest

to largest

• A numerical summary

• Measures the center of a distribution

• It is the value that has roughly the same number of observations above it and below it

• To measure the typical value in a data set, particularly when the distribution is skewed

IQR: tells us, roughly, how much space the middle 50% of the data occupy

• A numerical summary

• Measures the spread of the distribution of a data set

• Computes the distance taken up by the middle half of the sorted data

• To measure the variability in a sample, particularly when the distribution is skewed

Quartile: cuts in the distribution

Q1: roughly ¼ or 25% of the observations at or below it

Q2: roughly ½ or 50% at or below it, just another name for the median

Q3: roughly ¾ or 75% of the observations at or below it

Range: the distance spanned by the entire data set

3.4: Comparing Measures of Center

Resistant to Outliers: when the median is resistant to outliers, it is not affected by the size of

an outlier and does not change even if a particular outlier is replaced by an even more extreme

value

3.5: Using Boxplots for Displaying Summaries

Boxplots: shows the distribution divided into fourths. The left edge of the box is at Q1, and the

right edge is at Q3. The middle 50% of sorted observations lie inside the box. The length of the

box is proportional to the IQR

• A graphical summary

• Provides a visual display of numerical summaries of a distribution of numerical data

• The box stretches from the first quartile to the third quartile, and a vertical line indicates

the median. Whiskers extend to the largest and smallest values that are not potential

outliers, and potential outliers are indicated with special marks

• Boxplots are useful for comparing distributions of different groups of data

Potential Outliers: observations that are a distance of more than 1.5 interquartile ranges

Five Number Summary: the min, Q1, median, Q3, the max

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