December 15, 2014
8.4 Histograms and Shapes of Distributions
(12.4 Hand-out)
A histogram is a bar graph with no need of spaces between the bars since the
widths represent ranges of equally spaced intervals.For more on histograms click on
this link:
http://www.mathsisfun.com/data/histograms.html
Histogram (numerical data)
Bar Graph (categorical data)
Continuous x-axis --->
Intervals of 5
5
5
You describe the shapes of histograms like you did box-and-whisker plots:
Skewed right
Symmetric
Skewed left
(Also called "bell-shaped")
Note: The histogram to the left is a flat or uniform
distribution. A uniform distribution is also symmetric.
December 15, 2014
The shape of a distribution can be used to choose the most appropriate measure of
central tendency that describes a data set.
Symmetric
Skewed right
Skewed left
mean
mean ≈ median
median
*Use the mean as the
*Use the median as the
measure of central tendency
measure of central tendency
and the standard deviation
and the range or IQR to
to describe the spread.
describe the spread.
Note: If the histogram is symmetric then the
percentages of data that are one standard deviation
from the mean is typically 68%, the percentage two
standard deviations away is 95%, and within three
standard deviations is 99.7%.
Ex:
Heights of 250 Adult Females
median
mean
*Use the median as the
measure of central tendency
and the range or IQR to
describe the spread.
December 15, 2014
Ex:
p.630 Larson 2013