Empirical Rule, Z-Scores

Front

What is the Empirical Rule?

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 Z-score?

Back

A Z-score indicates how many standard deviations an element is from the mean. It is calculated as (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 one standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Front

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

Back

Approximately 95%.

Front

What percentage of data falls within three standard deviations of the mean in a normal distribution?

Back

Approximately 99.7%.

Front

If a Z-score is +2.00, what does it indicate about the data point?

Back

It indicates that the data point is 2 standard deviations above the mean.

Front

If a Z-score is -1.50, what does it indicate about the data point?

Back

It indicates that the data point is 1.5 standard deviations below the mean.

Front

What is the mean in a normal distribution?

Back

The mean is the average value of the dataset, where the data is symmetrically distributed.

Front

What is the standard deviation in a normal distribution?

Back

The standard deviation measures the amount of variation or dispersion of a set of values.

Front

What is the significance of a Z-score greater than +2 or less than -2?

Back

A Z-score greater than +2 or less than -2 is considered unusual, indicating that the data point is far from the mean.