Ch. 2 Review (2.1, 2.4, 2.5, 2.6)

Front

What is the mean in a data set?

Back

The mean is the average of all data points, calculated by summing all values and dividing by the number of values.

Front

What does standard deviation measure?

Back

Standard deviation measures the amount of variation or dispersion in a set of values.

Front

What is a percentile?

Back

A percentile indicates the value below which a given percentage of observations fall.

Front

What is the empirical rule in statistics?

Back

The empirical rule states that for a normal distribution, approximately 68% of data falls within one standard deviation of the mean, 95% within two, and 99.7% within three.

Front

If a test has a mean of 80 and a standard deviation of 9, what is the z-score for a score of 76?

Back

Z-score = (X - mean) / standard deviation = (76 - 80) / 9 = -0.44.

Front

What is the significance of a z-score?

Back

A z-score indicates how many standard deviations an element is from the mean; it helps in understanding the position of a score in a distribution.

Front

What percent of data lies within one standard deviation of the mean in a normal distribution?

Back

Approximately 68% of the data.

Front

How do you find the percent of people scoring below a certain value in a normal distribution?

Back

Use the z-score to find the corresponding percentile in the standard normal distribution table.

Front

What does it mean if a score is at the 55th percentile?

Back

It means that 55% of the scores are the same or lower than that score.

Front

What is the formula for calculating the z-score?

Back

Z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.