Normal Distribution Overview

The average value of a discrete probability distribution. It represents the expected value of the random variable.

The average value of all sample means. It's equal to the population mean.

The variance of the population divided by the sample size. It measures the spread of the sampling distribution.

The variance of the population divided by the sample size. It measures the spread of the sampling distribution.

A standardized score that measures how many standard deviations a data point is from the mean.

A continuous probability distribution that is symmetrical and bell-shaped. It describes how the values of a variable are distributed.

The mean, median, and mode of a normal distribution are all equal, meaning the data is clustered around the center.

The Central Limit Theorem states that even if a population's distribution isn't normal, the average of many random samples from that population will form a normal distribution.

The distribution is symmetrical, meaning both sides of the center are identical mirrors of each other.

The graph of a normal distribution resembles a bell shape.

The probability of finding a value closer to the mean is higher than finding a value further away.

The normal distribution is often referred to as the Gaussian distribution after Carl Friedrich Gauss, a prominent mathematician.

The normal distribution is a fundamental concept in statistics and probability theory, widely used in various fields like finance, engineering, and healthcare.

The process of converting raw data into z-scores, using the mean and standard deviation.

A chart showing the area under the standard normal curve, representing the probability of getting a z-score within a specific range.

The area under the standard normal curve between a z-score and the mean.

The area under the standard normal curve between two z-scores.

The area under the standard normal curve to the left or right of a z-score.

The total area under the standard normal curve is always 1, or 100%.

Identifying extreme values, typically outside of 3 standard deviations from the mean.

Represents the possible values a random variable can take and their corresponding probabilities.

A visual representation of a distribution, especially useful for large datasets.

Each probability value must be between 0 and 1, and the sum of all probabilities must equal 1.

Measures how spread out the data is from the mean. Variance is the average squared distance, and standard deviation is the average distance.

Represents the central tendency of a dataset.

The sum of all values divided by the number of values in the dataset.

The middle value when the dataset is ordered. If there's an even number of values, it's the average of the two middle values.

The value that appears most frequently in the dataset.

A type of random variable with countable outcomes, such as the number of heads in 5 coin flips. The outcomes are finite or countable.

A type of random variable with outcomes on a continuous scale, such as height or temperature. The outcomes are infinite and can be measured.

The percentage of data points that fall below a given value in a distribution.

Finding the area under the standard normal curve corresponding to a given Z-score to determine the percentile.

Finding the Z-score that corresponds to a given percentile rank.

Adding 0.5 to the area under the standard normal curve to the left of a positive Z-score or subtracting the area from 0.5 for a negative Z-score.

The process of transforming a raw score into a Z-score, which allows comparison across different distributions.

A statistical distribution where the mean, median, and mode are all located at the center. Its shape is symmetrical and resembles a bell.

The standard deviation determines the width of the normal curve. A larger standard deviation means a wider curve, indicating a larger spread of data.

The ends of the normal curve extend infinitely along the horizontal axis, getting closer to the baseline but never touching it.

The total area under a normal curve is always equal to 1. It represents the total probability of all data points within that distribution.

A standard normal curve has a mean of 0 and a standard deviation of 1.

The normal curve provides insights into the probability of observing different values within a dataset, aiding in making predictions and understanding trends.