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Chapter 4

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University of Toronto St. George

Statistical Sciences

STA220H1

Augustin Vukov

Fall

Description

Chapter 4
-We can display the distribution of quantitative data with a histogram, a stem-and-
lead display, or a dotplot
-We Tell what we see about the distribution by talking about shape, center, spread,
and any unusual features
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 (or
counts) falling into each bin
Histogram: Uses adjacent bars to show the distribution of a quantitative variable.
Each bar represents the frequency (or relative frequency) of values falling in each
bin
-Bins slice up all the values of the quantitative variable, so any spaces in a histogram
are actual gaps in the data, indicating a region where there are no observed values.
Relative frequency histogram: replacing counts on the vertical axis with the
percentage or proportion of the total number of cases falling in each bin
Stem-and-leaf: Shows quantitative data values in a way that sketches the
distribution of the data. Its like a histogram but it shows the individual values. They
work like histograms but they show more information.
Dotplots: places a dot along an axis for each case in the data. They are a great way
to display small data sets. They show basic facts about distribution.
When you describe a distribution you should always discuss three things:
1) Shape: to describe the shape of a distribution, look for:
Single versus multiple modes
Symmetry versus skewness
a) Does the histogram have a single, central hump or several separated humps?
These humps are called modes
One peak: unimodel {one mode}
Two peaks: bimodal {two modes}
Three or more peaks: multimodal {more than two modes}
Mode: a hump or local high point in the shape of the distribution of a
variable. The apparent location of modes can change as the scale of the
histogram is changed. Mode is the most frequent number occurring
b) Is the histogram symmetric{if the two halves on either side of the center
looks approximately like mirror images of eachother}? Can you fold it along a
vertical line through the middle and have the edges match pretty closely. The thinner ends of a distribution are called the tails. If one tail stretches out fur

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