Z-scores

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 from the mean.

Front

How do you calculate a Z-score?

Back

The formula for calculating a Z-score is: Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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 dataset.

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 significance of the area under the Z-score curve?

Back

The area under the Z-score curve represents the probability of a value occurring within a given range of the mean.

Front

What is the probability that a Z-score is less than 1.96?

Back

Approximately 97.5% of the data falls below a Z-score of 1.96 in a standard normal distribution.

Front

How do you find the probability of a Z-score being greater than a certain value?

Back

To find the probability of a Z-score being greater than a certain value, you can look up the Z-score in a standard normal distribution table and subtract that value from 1.

Front

What is the Z-score corresponding to the 95th percentile?

Back

The Z-score corresponding to the 95th percentile is approximately 1.645.

Front

What is the relationship between Z-scores and percentiles?

Back

Z-scores can be used to determine the percentile rank of a value in a normal distribution.