If a normal reference range for a test is given, then the mean and standard deviation can be derived if the statistical limits are known. The assumption is that the test shows a normal distribution.
Parameters:
(1) lower limit of reference range
(2) upper limit of reference range
(3) statistical limits to the reference range (95%, 97.5%, 98.8%, 99%)
upper limit =
= (mean) + ((number of standard deviations) * (standard deviation))
lower limit =
= (mean) - ((number of standard deviations) * (standard deviation))
mean value for the normal reference range =
= (lower limit) + (((upper limit) - (lower limit)) / 2) =
= ((upper limit) + (lower limit)) / 2
standard deviation =
= (((upper limit) - (lower limit)) / 2) / (number of standard deviations in the reference range) =
= ((upper limit) - (lower limit)) / (2 * (number of standard deviations))
Limits for the Reference Range |
Number of Standard Deviations |
68.27% |
1 |
95.45% |
2 |
97.5% |
2.25 |
98.8% |
2.5 |
99.73% |
3 |