Normal Curve Flashcards

Normal Distribution Overview

• Normal distribution is a bell-shaped, symmetrical curve with most scores clustering around the mean.
• Mean, median, and mode are identical in a normal distribution, emphasizing its symmetry.
• This distribution is widely applicable and assumed for many psychological and statistical variables.

Characteristics of Normal Distribution

• Mathematically defined and theoretical; real data may approximate this but not be perfectly normal.
• Mean, median, and mode reside at the 50th percentile.
• Both tail ends of the curve approach the x-axis but never actually intersect it.
• The total area under a standardized normal curve equals 1 (or 100%).
• Standard deviation (SD) can represent any positive value, affecting the width of the curve.

Understanding Percentiles and Z Scores

• Z scores translate standard deviations from the mean and allow for calculating population percentiles.
• A normal curve table provides accurate percentages of scores between any two Z points; for instance, 34% of scores lie between the mean and a Z score of 1.

Calculating Percentiles from Z Scores

• To find the percentile corresponding to a Z score:
  • Convert the raw score to a Z score, rounding to two decimal places.
  • Sketch the normal curve, shading the desired area (to the left or right of the Z score, or between two Z scores).
  • Use the normal curve table to identify the exact percentage, rounding down for conservative estimates.

Determining Z Scores from Percentiles

• To derive Z scores from a given percentile:
  • Draw a normal curve and shade the approximate area representing the target percentile.
  • Utilize the normal curve table to find the precise Z score.
  • Convert Z score back to raw score when needed, allowing for practical applications in real scenarios.