# STA 2023 Lecture Notes - Lecture 10: Interquartile Range, Unimodality, Standard Deviation

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School
Department
Course
Professor Distribution
The distribution of a quantitative variable slices up all the possible values of the variable into
equal width bins and gives the number of values falling into each bin
Histogram
A histogram uses adjacent bars to show the distribution of a quantitative variable. Each bar
represents the frequency of values falling in.
Gap
A region of the distribution where there are no values
Stem-and-leaf display
A Stem and leaf display shows quantitative data values in a way that sketches the distribution of
the data
Dotplot
a dot plot graphs a dot for each case against a single axis
Shape
To describe a distribution look for:
-single v. multiple modes
-symmetry v. skewness
-outliers and gaps
Center
The measures of center are mean and median
A numerical summary of how tightly the values are clustered around the center. Measures of
spread include the IQR and standard deviation.
Mode
A hump or local high point in the shape of a distribution of a variable. The apparent location of
modes can change as the scale of a histogram is changed.
Unimodal (Bimodal)
Having one mode.
Bi: two modes
Multi: many modes
Uniform
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Symmetric
A distribution is symmetric if the two halves on either side of the center look approximately like
mirror images of each other.
Tails
The tails of a distribution are the parts that typically trail off on either side.
Skewed
A distribution is skewed if it's not symmetric and one tail stretches out farther than the other.
Skewed left and right.
Outliers
Outliers are extreme values that don't appear to belong with the rest of the data.
Median
The median is the middle value, with half of the data above it and half below it. If n is even, it is
the average of the two middle values. It is usually paired with IQR.
Range
The difference between the lowest and highest values in a data set.
Quartile
The lower quartile is the value with a quarter of the data below it. The upper quartile is the value
with 3/4 of the data below it.
Interquartile Range
IQR. The difference between Q1 and Q2
5-number Summary
min
Q1
median
Q3
Max
Boxplot
A box plot displays the 5-number summary as a central box.
Mean
Mean is found by summing all the data points and dividing by the count
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