Normal Distribution

Front

What is Normal Distribution?

Back

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.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is the mean in a normal distribution?

Back

The average of all data points, which is the center of the distribution.

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Front

What is variance?

Back

A measure of how much values in a data set differ from the mean, calculated as the average of the squared differences from the mean.

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What is the standard deviation?

Back

The square root of the variance, representing the average distance of each data point from the mean.

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What does a Z-score represent?

Back

The number of standard deviations a data point is from the mean.

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What is the empirical rule (68-95-99.7 rule)?

Back

In a normal distribution, approximately 68% of data falls within 1 standard deviation, 95% within 2 standard deviations, and 99.7% within 3 standard deviations of the mean.

Tags

CCSS.HSS.ID.A.4

Front

How do you calculate the Z-score?

Back

Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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What is the significance of a Z-score of 0?

Back

A Z-score of 0 indicates that the data point is exactly at the mean.

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What percentage of data falls within 1 standard deviation of the mean in a normal distribution?

Back

Approximately 68%.

Tags

CCSS.HSS.ID.A.4

Front

What percentage of data falls within 2 standard deviations of the mean in a normal distribution?

Back

Approximately 95%.

Tags

CCSS.HSS.ID.A.4