A z-score indicates how many standard deviations an element is from the mean. It is calculated using the formula: $$z = \frac{x - \mu}{\sigma}$$ where x is the value, \mu is the mean, and \sigma is the standard deviation.

What is the formula for calculating the z-score of a sample?

The formula for calculating the z-score of a sample is: $$z = \frac{x - \bar{x}}{s}$$ where x is the value, \bar{x} is the sample mean, and s is the sample standard deviation.

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

A z-score of 0 indicates that the value is exactly equal to the mean.

How do you interpret a z-score of +2?

A z-score of +2 indicates that the value is 2 standard deviations above the mean.

How do you interpret a z-score of -1.5?

A z-score of -1.5 indicates that the value is 1.5 standard deviations below the mean.

What is the relationship between z-scores and standard deviations?

Z-scores express the position of a value in terms of standard deviations from the mean.

What is the z-score for a temperature of 17 degrees if the mean is 23 degrees and the standard deviation is 4.2 degrees?

The z-score is $$z = \frac{17 - 23}{4.2} = -1.43$$ .

What does it mean if a z-score is greater than 3 or less than -3?

A z-score greater than 3 or less than -3 indicates that the value is an outlier, being more than 3 standard deviations away from the mean.

What is the standard normal distribution?

The standard normal distribution is a normal distribution with a mean of 0 and a standard deviation of 1.

Resource Library

Math

Probability And Statistics

Z Score

Calculating Z Scores

Calculating Z-Scores

Flashcard

•

Mathematics

•

12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSS.ID.A.4

Standards-aligned

Wayground Content

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FLASHCARD QUESTION

Front

What is a z-score?

Back

FLASHCARD QUESTION

Front

How do you calculate a z-score for a population?

Back

FLASHCARD QUESTION

Front

What is the mean of z-scores?

Back

The mean of z-scores is always 0, regardless of the mean of the raw scores.

FLASHCARD QUESTION

Front

What does a positive z-score indicate?

Back

A positive z-score indicates that the value is above the mean.

FLASHCARD QUESTION

Front

What does a negative z-score indicate?

Back

A negative z-score indicates that the value is below the mean.

FLASHCARD QUESTION

Front

If the mean is 50 and the standard deviation is 10, what is the z-score for a value of 60?

Back

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