How to Calculate Reference Intervals

A reference range gives you an idea of what a normal measurement is for a particular data set. For example, knowing the reference range can help a school district determine appropriate placement in special education classes, or it could help a doctor decide whether lab test results are normal or abnormal. A reference range is calculated using the standard deviation (a measure of how spread out the data is) and the data’s mean (often called an “average”).

Things You'll Need

• Existing data, including standard deviation and mean

Instructions

1. Multiply the data set's standard deviation by 2. For example, if the standard deviation is 0.67, then 0.67 x 2 = 1.34.

2. Subtract your answer in Step 1 from the data's mean. This is the lower value of the reference interval. For example, if your mean is 4.06, then 4.06 - 1.34 = 2.72.

3. Add your answer from Step 1 to the data's mean. This is the upper value of the reference interval. For example, if your mean is 4.06, then 4.06 + 1.34 = 5.4. Since the reference interval is an interval centered on the mean, plus or minus 2 sigma, we're done; our interval is {2.72, 5.4}.

Tips & Warnings

• Modern graphing calculators will automatically calculate the mean and standard deviation for a data set.

References

• York University: Reference Interval

Resources

• Statistics How To: TI-83 Standard Deviation