z scores assessment

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

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

How do you calculate a z-score?

Back

The z-score is calculated using the formula: z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

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 standard deviation in the z-score formula?

Back

The standard deviation in the z-score formula serves as a measure of the dispersion or spread of the data points in the distribution.

Front

What is the area under the normal curve?

Back

The area under the normal curve represents the total probability of all possible outcomes, which equals 1.

Front

What does the area between the mean and a z-score represent?

Back

The area between the mean and a z-score represents the probability of a score occurring within that range.

Front

What is the relationship between z-scores and percentiles?

Back

Z-scores can be used to determine percentiles, which indicate the percentage of scores that fall below a particular score in a distribution.

Front

What is the probability of a score occurring if its z-score is +1.50?

Back

If the z-score is +1.50, the probability of a score occurring is approximately 93.32%, meaning it is higher than 93.32% of the scores in the distribution.