Understanding Z-Scores and Distributions

The video tutorial covers module 3.2, focusing on the empirical rule and z-scores. It begins with a review of key concepts from module 3.1, including population, sample, and statistical measures. The tutorial then explains the normal distribution, its characteristics, and the empirical rule, which describes data distribution within standard deviations. Examples illustrate the application of the empirical rule and z-scores in data analysis, emphasizing their use in comparing data sets and understanding data spread.

Which of the following is not resistant to outliers?

• Mean

• Third quartile

• Median

• First quartile

What type of graph is used to show the shape, central tendency, and dispersion of quantitative data?

• Histogram

• Bar chart

• Pie chart

• Line graph

In a symmetric and unimodal distribution, which measures of center are equal?

• Mean and median

• Mean and mode

• Median and mode

• Mean, median, and mode

What percentage of data falls within one standard deviation of the mean in a normal distribution?

• 99.7%

• 95%

• 50%

• 68%

What is the z-score formula?

• z = (x + mean) / standard deviation

• z = (x - mean) / standard deviation

• z = (mean - x) / standard deviation

• z = (x - mean) * standard deviation

If a z-score is positive, what does it indicate about the data point?

• It is below the mean

• It is above the mean

• It is an outlier

• It is equal to the mean

What is the unit of a z-score?

• Degrees

• Percentages

• Standard deviations

• Meters

How many standard deviations away from the mean is a z-score of 3?

• 3

• 1

• 2

• 4

Which of the following best describes a standardized score?

• A score that compares different data sets

• A score that is always positive

• A score that is equal to the mean

• A score that is always negative

In comparing two data sets using z-scores, what does a higher z-score indicate?

• The data point is an outlier

• The data point is at the mean

• The data point is further from the mean

• The data point is closer to the mean