A normal distribution is a probability distribution that is symmetric around the mean, showing that data near the mean are more frequent in occurrence. It forms a bell-shaped curve where most of the observations cluster around the central peak.
congrats on reading the definition of normal distributions. now let's actually learn it.
The mean, median, and mode of a normal distribution are all equal.
The total area under the curve of a normal distribution is equal to 1.
Approximately 68% of data falls within one standard deviation from the mean in a normal distribution.
The standard deviation determines the width of the bell curve; larger standard deviations result in wider curves.
Normal distributions are used in various statistical methods, including hypothesis testing and confidence intervals.
Review Questions
What percentage of data falls within one standard deviation from the mean in a normal distribution?
How do the mean, median, and mode compare in a normal distribution?
Why is the area under the curve of a normal distribution always equal to 1?
Related terms
Standard Deviation: A measure of how spread out numbers are from the mean.
Z-Score: The number of standard deviations an element is from the mean.
Central Limit Theorem: States that with a large enough sample size, the sampling distribution of the sample mean will be normally distributed regardless of the original population's distribution.