STA 2023 Lecture Notes - Lecture 10: Interquartile Range, Unimodality, Standard Deviation
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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
A histogram uses adjacent bars to show the distribution of a quantitative variable. Each bar
represents the frequency of values falling in.
A region of the distribution where there are no values
A Stem and leaf display shows quantitative data values in a way that sketches the distribution of
a dot plot graphs a dot for each case against a single axis
To describe a distribution look for:
-single v. multiple modes
-symmetry v. skewness
-outliers and gaps
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.
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.
Having one mode.
Bi: two modes
Multi: many modes
A distribution that is roughly flat is said to be uniform.
A distribution is symmetric if the two halves on either side of the center look approximately like
mirror images of each other.
The tails of a distribution are the parts that typically trail off on either side.
A distribution is skewed if it's not symmetric and one tail stretches out farther than the other.
Skewed left and right.
Outliers are extreme values that don't appear to belong with the rest of the data.
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.
The difference between the lowest and highest values in a data set.
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.
IQR. The difference between Q1 and Q2
A box plot displays the 5-number summary as a central box.
Mean is found by summing all the data points and dividing by the count