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Chapter 3.3-3.5

# MATH 10041 Chapter Notes - Chapter 3.3-3.5: QuartilePremium

1 pages23 viewsSpring 2019

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