FLASHCARD: Normal Distribution and Measures of Dispersion

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Front

What is a normal distribution?

Back

A normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean.

Front

What does the mean represent in a normal distribution?

Back

The mean is the average of all data points in a distribution and is the center point of a normal distribution.

Front

What is standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values. A low standard deviation means that the values tend to be close to the mean, while a high standard deviation means that the values are spread out over a wider range.

Front

How do you calculate the z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

Front

What percentage of data falls within two standard deviations in a normal distribution?

Back

Approximately 95% of the data falls within two standard deviations of the mean in a normal distribution.

Front

What is the significance of a z-score of 1.33?

Back

A z-score of 1.33 indicates that the value is 1.33 standard deviations above the mean.

Front

What is the formula for calculating standard deviation?

Back

The formula for standard deviation is: σ = √(Σ(X - μ)² / N), where Σ is the sum, X is each value, μ is the mean, and N is the number of values.

Front

What does it mean if a data set is normally distributed?

Back

If a data set is normally distributed, it means that the data follows a bell-shaped curve, where most of the observations cluster around the central peak and probabilities for values further away from the mean taper off equally in both directions.

Front

What is the relationship between mean, median, and mode in a normal distribution?

Back

In a normal distribution, the mean, median, and mode are all equal and located at the center of the distribution.