# Susan Verdin

## Properties of a Normal Curve

Important Properties of a normal curve are:
• The curve is bell shaped, with the highest point over mean.
• The curve is symmetrical about a vertical line through mean.
• Curve approaches horizontal axis but never touches it.
• The inflection(transition) points between cupping upward and downward occur above mean + standard deviation and mean - standard deviation.
• The area under the entire curve is 1.

## The Mean and Standard Deviation

• On the graph, the mean is always in the middle.
• The left side of the mean is positive, and the right side is negative.
• The area between mean - SD and mean + SD equals 34%
• The area between mean - 2SD and mean + 2SD equals 13.5%
• The area between mean - 3SD and mean + 3SD equals 2.35%
• Anything beyond is 0.15%

## The Empirical Rule

• 68% of data values lie within 1 standard deviation on each side of the mean.
• 95% of data values lie within 2 standard deviations on each side of the mean.
• 99.7% of all data values within 3 standard deviations on each side of the mean.

## Control Chart

Control charts are charts that show data over space time intervals. For example, how much weight a person loses in 30 days. The chart helps the person losing weight to see their progress over time. A bad control chart would be an "Out-of-Control Chart"

## Z Scores, Standard Scores, and Raw Scores

A Z-Score is a statistical measurement of a score's relationship to the mean in a group of scores. A Z-Score of 0 means the score is the same as the mean. A Z-Score can also be positive or negative, indicating whether it is above or below the mean and by how many standard deviations. When given mean and SD, the data can be converted to Z-Scores, Raw scores, or Standard scores.

## How to find a Z-Score

In the back of the textbook, the Appendix II charts help find the matching data for the Z score.