High School Math : Understanding Z-Scores

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : Understanding Z Scores

What is the -score for a value of 115 when the mean of the population is 103 and the standard deviation is 8?

Possible Answers:

Correct answer:

Explanation:

-score indicates whether a particular value is typical for a population or data set.  The closer the -score is to 0, the closer the value is to the mean of the population and the more typical it is.  The -score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation. 

 

Example Question #2 : Understanding Z Scores

A value has a -score of .  The value is . . .

Possible Answers:

two standard deviations from the population mean

the same as the population mean

one standard deviation from the population mean

below the population mean

above the population mean

Correct answer:

below the population mean

Explanation:

The -score indicates how close a particular value is to the population mean and whether the value is above or below the mean.  A positive -score is always above the mean and a negative -score is always below it.  Here, we know the value is below the mean because we have a negative -score.

Example Question #2 : Data Sets And Z Scores

A population of values has a mean of 43 and a standard deviation of 12.  One of the values in the population is 49.  What is the Z-score for that value?

Possible Answers:

Correct answer:

Explanation:

A Z-score indicates whether a particular value is typical for a population or data set.  The closer the Z-score is to 0, the closer the value is to the mean of the population and the more typical it is.  The Z-score is calculated by subtracting the mean of a population from the particular value in question, then dividing the result by the population's standard deviation.

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