This is somewhat more tedious to perform, but may be useful for example in cases where a study that establishes a reference range presents only the arithmetic mean and standard deviation, leaving out the source data. If the original assumption of arithmetically normal distribution is shown to be less appropriate than the log-normal one, then, using the arithmetic mean and standard deviation may be the only available parameters to correct the reference range. By assuming that the expected value can represent the arithmetic mean in this case, the parameters "μlog" and "σlog" can be estimated from the arithmetic mean ("m") and standard deviation ("s.d.") as:  Following the exampled reference group from the previous section:  Subsequently, the logarithmized, and later non-logarithmized, lower and upper limit are calculated just as by logarithmized sample values. Reference ranges can also be established directly from the 2.5th and 97.5th percentile of the measurements in the reference group. For example, if the reference group consists of 200 people, and counting from the measurement with lowest value to highest, the lower limit of the reference range would correspond to the 5th measurement and the upper limit would correspond to the 195th measurement. This method can be used even when measurement values do not appear to conform conveniently to any form of normal distribution or other function. However, the reference range limits as estimated in this way have higher variance, and therefore less reliability, than those estimated by an arithmetic or log-normal distribution (when such is applicable), because the latter ones acquire statistical power from the measurements of the whole reference group rather than just the measurements at the 2.5th and 97.5th percentiles. Still, this variance decreases with increasing size of the reference group, and therefore, this method may be optimal where a large reference group easily can be gathered, and the distribution mode of the measurements is uncertain. In case of a bimodal distribution (seen at right), it is useful to find out why this is the case. Two reference ranges can be established for the two different groups of people, making it possible to assume a normal distribution for each group. This bimodal pattern is commonly seen in tests that differ between men and women, such as prostate specific antigen. In case of medical tests whose results are of continuous values, reference ranges can be used in the interpretation of an individual test result. This is primarily used for diagnostic tests and screening tests, while monitoring tests may optimally be interpreted from previous tests of the same individual instead.