Normal Distribution
EDP column by Dr Ketan Dhatariya

“I had some blood tests at my doctors. They showed me some of the results – and some of them had been highlighted as abnormal – but my GP told me not to worry because they were only just outside the normal range. Where does the normal range come from?”

Technically speaking the correct term is the ‘reference range’, and not the ‘normal range’. The reason for this is that even though a person can get a result outside of the range, they may still be ‘normal’, or people who fall within the range may still be ‘abnormal’.  The explanation for this can be a little tricky.

The reference range is a set of values of some measurement that can be used to interpret a result for any particular individual. The range is derived by testing lots of people – maybe hundreds or thousands – who have no evidence of illness or disease. If the results are plotted, with those results that occur most frequently; or the average result; lying in the middle, then there will be equal numbers of results falling on either side of the most frequently occurring result. Those results that occur least frequently lie furthest from those that occur most frequently. The shape of the graph that is plotted is known by several names, including a ‘normal distribution curve’, a ‘bell shaped curve’ or a ‘Gaussian curve’, named after the German mathematician Johann Gauß (1777 – 1855). If you remember your maths from school, this is the kind of curve where the average (the mean), the number in the middle (the median) and the most frequently occurring number (the mode), are all the same.

Mathematicians then did a statistical calculation on the curve to include as many ‘normal’ people as they could. This statistical calculation – known as a ‘standard deviation’ – when doubled – includes 95% of all of the numbers evenly spread around the result that occurs most frequently. This is the reference range – “all values that occur within 2 standard deviations either side of the mean”. However, what this means is that there are still 2.5% of people who will have results higher than the upper limit of the reference range that are still ‘normal’, as well as a further 2.5% who have results lower than the lower end of the reference range. Taken another way, statistically speaking, if 20 things are measured, by chance alone, 1 of the results will be fall outside the reference range. 

Your doctor will usually be familiar with the reference ranges for the tests that you have had done. As always, if you are concerned or do not understand what your doctor has said to you, ask them to explain it to you in a way that you do understand.