Understanding Z-Scores

This video tutorial introduces z-scores, explaining how they measure the distance of a data point from the mean in terms of standard deviations. It provides examples of calculating z-scores for both positive and negative values and demonstrates how to determine a test score from a given z-score. The tutorial also covers using z-score tables to find the percentage of data above or below a certain score, highlighting the symmetry of the normal distribution.

What is a z-score used to describe in a data set?

• The average value of the data set

• The number of data points

• The sum of all data values

• How far a data value is from the mean

In the first example, what is the z-score for a score of 152 if the mean is 130 and the standard deviation is 20?

• 3.0

• 0.5

• 2.2

• 1.1

What does a positive z-score indicate about a data value?

• It is an outlier

• It is below the mean

• It is equal to the mean

• It is above the mean

In the second example, what is the z-score for a score of 29 if the mean is 125 and the standard deviation is 40?

• -2.4

• -1.5

• -3.0

• -0.8

What does a negative z-score indicate about a data value?

• It is above the mean

• It is an outlier

• It is equal to the mean

• It is below the mean

How do you calculate a score from a given z-score, mean, and standard deviation?

• Divide the z-score by the standard deviation

• Multiply the z-score by the mean

• Add the z-score to the mean

• Multiply the z-score by the standard deviation and add to the mean

If a z-score is 1.5, what percentage of data is below this score according to the cumulative table?

• 50%

• 99.7%

• 93.32%

• 68.27%

In the advanced example, what is the score corresponding to a z-score of -2.1 if the mean is 100 and the standard deviation is 40?

• 60

• 80

• 20

• 16

How can you find the percentage of data above a negative z-score using a z-score table?

• Subtract the z-score from 100

• Use the zero through z table and symmetry

• Add the z-score to 50

• Use the cumulative table directly

What percentage of data is above a score of 16 if the z-score is -2.1?

• 98.21%

• 50%

• 0.5%

• 1.79%