Transcript Density curves

Density curves
• Like drawing a curve through the tops of the
bars in a histogram and smoothing out the
irregular ups and downs.
• Show the proportion of observations in any
region by the area under the curve
• Choose a scale so that the total area under the
curve is 1
The center and spread of a density
curve
• The median is the equal-areas point—the point
that divides the area under the curve in half
• The mean is the balance point, at which the
curve would balance if made of solid material
• The mean and median of a symmetric curve
are in the same place
• The mean of a skewed curve is pulled toward
the long tail
The normal distribution
• Normal curves are symmetric, single-peaked,
and bell-shaped.
• A normal curve can be described completely
by its mean and standard deviation
• The standard deviation determines the shape of
the curve
• Distributions of many scientific variables end
up being normal
• The 68-95-99.7% rule
Standard scores
• Standard scores are scores that are expressed
in standard deviations above or below the
mean
• Standard score = (observation –mean) /std. dev
Percentiles
• The xth percentile of a distribtuion is a value such
that x percent of the observations lie below it and the
rest above it.
• Median = 50% percentile
• Quartiles = ?
• Standard scores translate into specific percentiles that
are not affected by the mean and standard deviation
• Finding the observation that matches a percentile