Understanding Z-Scores and Their Interpretations

What is the formula for finding the z-score?

• z = (X - σ) / μ
• z = (X + μ) / σ
• z = (X - μ) / σ
• z = (μ - X) / σ

Which of the following is the correct interpretation of a z-score?

• The average of all data points in a dataset

• The sum of all data points divided by the number of data points

• The difference between the highest and lowest data points

• The number of standard deviations a data point is from the mean

If a data point has a z-score of 2, what does this imply?

• The data point is two standard deviations below the mean

• The data point is two standard deviations above the mean

• The data point is at the mean

• The data point is an outlier

What are the percentiles to know on a CRF graph?

• 25th, 50th, and 75th percentiles
• 5th, 15th, and 95th percentiles
• 10th, 30th, and 90th percentiles
• 20th, 40th, and 60th percentiles

Answer explanation

Q1-25th

Q2-50th(median)

Q3-75th

What is a Z-score?

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If a distribution is right skewed, what does that mean?

• It means that the distribution has a longer tail on the left side.
• It indicates that the median is less than the mean.

• It means that the distribution has a longer tail on the right side.
• It suggests that most values are concentrated on the right side.
• I don't know.

If a distribution is left skewed, what does it mean?

• It means that the distribution has a longer tail on the right side.
• The mean is less than the median.

• It means that the distribution has a longer tail on the left side.
• It suggests that the data is uniformly distributed.
• I don't know.

If a distribution is symmetric, what does that mean?

• A symmetric distribution is always uniform in shape.
• A symmetric distribution has equal values on both sides of its center.
• A symmetric distribution has unequal values on both sides.
• A symmetric distribution has a single peak on one side.
• Mean=Median

Describe the effect of adding, subtracting, multiplying by, or dividing by a constant on the shape, center, and variability of a distribution.

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What's the total area of a density curve?

• 1.5
• 2
• 0.5
• 1