Question

a set of data has a mean of 12 and a standard deviation of 3. a data point of the set has a z-score of 1.3. what does a z-score of 1.3 mean?

the data point is 1.3 standard deviations away from 3
the data point is 1.3 standard deviations away from 12
the data point is 3 standard deviations away from 1.3
the data point is 3 standard deviations away from 12

Explanation:

Define the meaning of a z-score

A z-score measures the number of standard deviations a specific data point is from the mean of the data set.

Apply the definition to the given values

Using the Z-Score Formula concept, we are given:

• Mean (\(\mu\)) = \(12\)
• Standard deviation (\(\sigma\)) = \(3\)
• Z-score (\(z\)) = \(1.3\)

A z-score of \(1.3\) means that the specific data point lies exactly \(1.3\) standard deviations away from the mean, which is \(12\).

Match with the given options

• Option 1: "The data point is 1.3 standard deviations away from 3" (Incorrect, 3 is the standard deviation, not the mean).
• Option 2: "The data point is 1.3 standard deviations away from 12" (Correct, 12 is the mean).
• Option 3: "The data point is 3 standard deviations away from 1.3" (Incorrect).
• Option 4: "The data point is 3 standard deviations away from 12" (Incorrect).

Answer:

• The data point is 1.3 standard deviations away from 3
• The data point is 1.3 standard deviations away from 12 (Correct answer)
• The data point is 3 standard deviations away from 1.3
• The data point is 3 standard deviations away from 12