Normal distribution

Definition

A normal distribution is a continuous probability distribution that is symmetrical around its mean, with a characteristic bell-shaped curve. In a normal distribution, most of the data points are concentrated around the mean, and the probabilities for values further away from the mean taper off equally in both directions.

5 Must Know Facts For Your Next Test

1. The mean, median, and mode of a normal distribution are all equal.
2. Approximately 68% of the data in a normal distribution falls within one standard deviation of the mean.
3. The total area under the curve of a normal distribution is equal to 1.
4. Normal distributions are defined by two parameters: mean ($\mu$) and standard deviation ($\sigma$).
5. The Z-score represents the number of standard deviations a data point is from the mean.

Review Questions

• What percentage of data falls within one standard deviation of the mean in a normal distribution?
• How are the mean, median, and mode related in a normal distribution?
• What do $\mu$ and $\sigma$ represent in a normal distribution?

Related terms

Z-Score: A Z-score indicates how many standard deviations an element is from the mean.

Standard Deviation: A measure of the amount of variation or dispersion in a set of values.

$t$ Distribution: $t$ Distribution is similar to a normal distribution but has heavier tails, used especially when dealing with small sample sizes.