Density Curves and Normal Distributions
STAT 110: Chapter 13
Hitchcock
Density Curves and Normal Distributions
? Recall: For data on a quantitative variable, the histogram gives a
graphical picture of the distribution.
? Histogram will show us approximate shape, center, spread, and any
outliers
? In addition, numerical measures (like 5-number summary) can
describe the distribution.
? Note: A histogram is designed to summarize a sample of data.
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STAT 110: Chapter 13
Hitchcock
Density Curves
? A density curve is a graphical picture of the population distribution
of a variable.
? Resembles a histogram, but a histogram looks "blocky" (because
of the bars)
? Density curve is usually a smooth curve. ? Density curve is like a smoothed-out, idealized version of a histogram.
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STAT 110: Chapter 13
Example of a Density Curve:
An example density curve
Hitchcock
0.5
0.4
0.3
Density
0.2
0.1
0.0
2
3
4
5
6
7
Variable Values
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STAT 110: Chapter 13
Hitchcock
More on Density Curves
? Histograms may plot counts or proportions on vertical axis ? Density curves always deal with proportions of data, but the
plotting is done a bit differently.
? A proportion of data is represented by a certain area under the
density curve.
? Total area under a density curve is always 1 (Total proportion = 1).
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STAT 110: Chapter 13
Recall the Student Weight Variable:
Possible density curve for the weight variable
Hitchcock
0.010
0.008
Density 0.004 0.006
0.002
0.000
100
150
200
250
Weight
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