2.1 - 2.4 Review (Percentiles, Z-Scores, and Empirical Rule)

Front

What is a percentile?

Back

A percentile is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations falls.

Front

What does a Z-score represent?

Back

A Z-score indicates how many standard deviations an element is from the mean of the dataset.

Front

What is the Empirical Rule?

Back

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

Front

Calculate the Z-score for a value of 10.07 seconds, given a mean of 10.3293 seconds and a standard deviation of 0.2709 seconds.

Back

Z = (X - μ) / σ = (10.07 - 10.3293) / 0.2709 = -0.9572.

Front

If you scored at the 55th percentile, what does this imply about your performance relative to your peers?

Back

It implies that 55% of the class scored below your score.

Front

According to the Empirical Rule, what percentage of data falls within 2 standard deviations of the mean?

Back

Approximately 95% of the data falls within 2 standard deviations of the mean.

Front

What is the range of tire life for 68% of tires if the mean life is 30,000 km and the standard deviation is 2000 km?

Back

The range is from 28,000 km to 32,000 km.

Front

In a symmetric distribution, how do the mean and median compare?

Back

In a symmetric distribution, the mean and median are equal.

Front

What percentage of data falls within 1 standard deviation of the mean according to the Empirical Rule?

Back

Approximately 68% of the data falls within 1 standard deviation of the mean.

Front

If a dataset has a mean of 50 and a standard deviation of 5, what is the Z-score for a value of 60?

Back

Z = (60 - 50) / 5 = 2.