Normal Distribution Notes

Normal Distribution

Characteristics of Normal Distribution

  • The normal distribution isn't a single entity but rather a family of distributions.
  • They are symmetrical.
  • Data clusters around the center.
  • The mean, median, and mode are aligned; they all coincide at the center of the distribution.

Examples of Normal Distribution

  • NBA Player Heights: The average height in the NBA is 6 feet 7 inches.
  • General Population Heights: NBA players represent a small fraction of the overall population's height distribution.
  • Age Distribution: A 30-year-old’s height compared to the population.

Distribution Shape

  • Ends of distribution (very tall or short) have small numbers
  • Most data points are bunched around the middle.
  • Symmetrical: Very few seven-footers; Very few five-footers

Mode in Normal Distribution

  • Mode: The most frequently occurring score within the distribution.
  • In a symmetrical distribution, the mode falls right around the middle.

Median in Normal Distribution

  • Median: The middle value of the distribution.
  • In a symmetrical distribution, the median falls right around the middle, too.

Mean in Normal Distribution

  • Mean: The mathematical average of the scores.
  • In a normal distribution, the mean falls right around the middle, matching the median and mode.

Implications of Mean, Median, and Mode Location

  • For normal distributions, mean, median, and mode cluster in the center.

Standard Deviation and Percentage of Population

  • If we know the standard deviation, we can determine the percentage of people that fall at a certain place above or below a certain score.

Standard Deviations

  • Zero represents the mean.
  • One standard deviation above and below represented.
  • Two standard deviations above and below represented.

Intelligence and IQ scores

  • If you collect scores from a large population, it's going to look similar to this.
  • Above two standard deviations above the mean, you have a really small part of the population.
  • Below two standard deviations, you have a really, really small part of the population.
  • Most people fall right around the mean or one standard deviation above and below.

Distribution Tail

  • The tail of the distribution never quite touches the bottom of the chart.
  • Theoretically, a distribution goes out on each tail in an infinite manner.

Normal Distribution Importance

  • This is so important because where building towards something.
  • We're not talking about hypothesis testing yet, but you have to understand the basic understanding of the distribution and how you create standard scores in order to understand how hypothesis testing works.

Application: Standardized Tests / Standard Scores

  • Standard deviations and the normal curve allow us to help determine how many individuals fall above or below a specific point.
  • Raw scores are meaningless.
  • Critical to relate individual performance to the performance of all students in their group.
  • Must relate standard deviation and normal curve to understanding standard scores.