To convert z-score for a number above the mean to percentile, use the Standard Normal Table to find the area beyond Z and subtract this area from 1.00. Multiply the result by 100 to get the percentile. To convert z-score for a number below the mean, skip the subtraction step prior to multiplication.
- Consult a z-score chart
Z-score charts are available online and in any Statistics textbook.
- Determine if the raw score is above or below the mean
Z-scores below the mean are expressed as negatives. Z-scores above the means are expressed as positives. There are two separate charts for z-scores above and z-scores below the mean.
- Find the z-score value on the chart
Z-scores are expressed through the tenths decimal on the vertical axis. The hundredths place is expressed across the horizontal axis. Trace the row of the score measured by tenths to where it meets the column of the hundredths. The number in that box is the z-score.
- Compute percentile based on the correct formula
Remember that the formula for converting a z-score to percentile for a number on the negative z-score chart only requires multiplying the number on the chart by 100. Converting positive z-scores has the additional step of subtracting the charted number from one first.