12-4 Normal Distribution

Normal Distribution Curve A normal distribution curve is symmetrical, bell-shaped curve defined by the mean and standard deviation of a data set.

The Bell Curve   One standard deviation away from the mean ( in either direction on the horizontal axis accounts for around 68 percent of the data. Two standard deviations away from the mean accounts for roughly 95 percent of the data with three standard deviations representing about 99.7 percent of the data.  

Skewed Distributions The distribution is positively skewed if the “lump” is to the left of center. The distribution is negatively skewed if the “lump” is to the right of center.

Official Definition An outlier is any data point that is more than 1.5 standard deviations from the mean.

Example #1 Approximately what percent of students are between 84 and 95 pounds? 20% + 13% = 33% 25 20 Percent of Students 15 10 5 60-65 66-71 72-77 78-83 84-89 90-95 96-101 Weight (lbs)

Example #2 Sketch a normal curve for a data set with a mean of 50 and a standard deviation of 4. (Label the x-axis values at one, two and three standard deviations from the mean). 50 38 42 46 54 58 62