Interpreting 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.

Front

How do you calculate a z-score?

Back

Z-score = (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 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?

Back

Z-scores are used to describe the exact location of a score within a distribution.

Front

If a jar candle has a mean burn time of 25 hours and a standard deviation of 2.5 hours, what is the burn time for a z-score of 1.5?

Back

Burn time = μ + (z * σ) = 25 + (1.5 * 2.5) = 28.75 hours.

Front

If a pillar candle has a mean burn time of 95 hours and a standard deviation of 7.5 hours, what is the burn time for a z-score of 1.5?

Back

Burn time = μ + (z * σ) = 95 + (1.5 * 7.5) = 106.25 hours.

Front

What percentage of values lie below a z-score of -1?

Back

Approximately 16% of values lie below a z-score of -1 in a standard normal distribution.

Front

What is the empirical rule in relation to z-scores?

Back

The empirical rule states that for a normal distribution, about 68% of values lie within 1 standard deviation of the mean, 95% within 2 standard deviations, and 99.7% within 3 standard deviations.