Overview
This lecture introduces types of frequency distributions, focusing on the normal distribution, skewed distributions, bimodal and rectangular distributions, and explains the concepts of relative frequency and percentiles in the context of a normal curve.
Types of Frequency Distributions
- The normal distribution is an ideal, symmetrical, bell-shaped curve centered around the mean.
- Most scores cluster around the mean, with fewer scores appearing at the extremes (tails) of the distribution.
- The normal distribution is a key assumption for many statistical tests.
Skewed Distributions
- Skewed distributions are asymmetrical, differing from the normal distribution.
- A negatively skewed distribution has a pronounced tail on the left (low scores) and most scores on the higher end.
- A positively skewed distribution has a pronounced tail on the right (high scores) and most scores on the lower end.
- Examples of negative skew: age of death, long jump distances.
- Examples of positive skew: hospital stay duration, household income.
Other Distribution Types
- Bimodal distributions have two high-frequency “peaks” or modes, indicating two common score ranges.
- Rectangular distributions have all frequencies roughly equal, showing no mode.
Normal Distribution and Percentiles
- Percentiles show the percentage of scores below a specific value in a distribution.
- In a normal distribution, the area under the curve to the left of a score indicates its percentile rank.
- The 50th percentile (median) is at the midpoint of the distribution.
- For example, 30 may represent the 50th percentile, 20 the 15th percentile, and 45 the 85th percentile.
Relative Frequency
- Relative frequency represents the proportion of scores occurring within a specific range compared to all scores.
- The area under the curve for a range of scores equals their combined relative frequency.
Key Terms & Definitions
- Normal distribution — Symmetrical, bell-shaped distribution where most values cluster around the mean.
- Skewed distribution — Asymmetrical distribution with a pronounced tail on one side.
- Negatively skewed — Tail on the left (low scores), most data on the right.
- Positively skewed — Tail on the right (high scores), most data on the left.
- Bimodal distribution — Distribution with two peaks or modes.
- Rectangular distribution — Distribution where all outcomes have equal frequency.
- Percentile — The percentage of values in a distribution that fall below a given score.
- Relative frequency — The proportion of occurrences for a score or range relative to the total.
Action Items / Next Steps
- Review examples of different distributions in your textbook.
- Prepare for further discussions on normal distributions, percentiles, and their applications in upcoming chapters.