Finding Z - Score

Front

What is a Z-score?

Back

A Z-score is a statistical measurement that describes a value's relationship to the mean of a group of values, expressed in terms of standard deviations.

Front

How do you calculate a Z-score?

Back

Z-score = (X - Mean) / Standard Deviation, where X is the value, Mean is the average of the dataset, and Standard Deviation measures the dispersion.

Front

What does a Z-score of 0 indicate?

Back

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

Front

What does a positive Z-score indicate?

Back

A positive Z-score indicates that the data point is above the mean.

Front

What does a negative Z-score indicate?

Back

A negative Z-score indicates that the data point is below the mean.

Front

What is the purpose of Z-scores in statistics?

Back

Z-scores are used to describe the exact location of a score within a distribution, allowing for comparison between different datasets.

Tags

CCSS.HSS.ID.A.4

Front

If the mean is 22.8 and the standard deviation is 7, what is the Z-score for x = 20?

Back

Z-score = (20 - 22.8) / 7 = -0.4.

Front

If the mean is 21 and the standard deviation is 1.3, what is the Z-score for x = 22?

Back

Z-score = (22 - 21) / 1.3 = 0.77.

Front

If the mean is 29.8 and the standard deviation is 7, what is the Z-score for x = 20?

Back

Z-score = (20 - 29.8) / 7 = -1.4.

Front

If the mean is 27 and the standard deviation is 1.4, what is the Z-score for x = 11?

Back

Z-score = (11 - 27) / 1.4 = -11.43.