Standard Scores on the Normal Curve

Standard scores are ways to measure positions on the normal curve. They are standard because the size of the distribution or type of measurement, they always fall in the same place. They include standard deviations, percentile ranks, T-scores, and deviation IQs.

The percentages of the area under the normal curve are the same for each standard deviation. Once you calculate the standard deviation for any set of scores, you can find any standard score for the data set. You can also figure out where any score falls relative to others.

Let's use IQ as an example (go the very bottom of the graphic). Intelligence quotients have a mean of 100 and a standard deviation of 15. If your IQ is 100, you fall right on the mean for standard IQ scores. Sixty-eight percent of the population is within plus or minus one deviation of 100.

The Normal Curve

Standard Scores

If your IQ is above 130, or two deviations above the mean, you are among only about 2.5% of the population. This is one way for schools to decide whether or not you would meet the criteria for being placed in the gifted class.

Z-scores place the mean at "0". Each deviation is counted as "1" from the mean, plus or minus.

T-scores place the mean at "50" with deviations of "10" each.

If a teacher tells a parent that their child achieved a z-score of -1 on a reading assessment, the parent may not understand exactly what that means. But it is much easier to understand a T-score of 40 where the average is 50.

Percentiles are not percentages. Percentiles also have a mean of 50, where 50% of the population falls below that point. A percentile rank of 99% means that 99% of the population falls below that score on the normal curve.

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