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 % 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