### All High School Math Resources

## Example Questions

### Example Question #1 : How To Find Z Scores For A Data Set

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:**

A -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 #1 : 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

below the population mean

one standard deviation from the population mean

above the population mean

**Correct answer:**

below the population mean

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 #1 : Continuous Distributions

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:**

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.