Required section · Section 2 of 6
Mean as center, SD as spread, under stated conditions
The mean is the arithmetic center of a defined set of observations. It is a property of this particular dataset, under its stated conditions, not a fixed property of the analyzer that will hold no matter what changes. Change the lot, the day, the operator, or the time window, and you have a different dataset, which can produce a different mean even if nothing is actually wrong.
A sample mean is also an estimate. It estimates whatever longer-run process generated the data, and a different sample drawn from that same process can land on a different mean just from sampling variation. Five results is a small sample; treat the mean it produces as a snapshot, not a settled constant.
Standard deviation describes the spread of observations around their mean, and it carries the same unit as the result. A small SD means the five results cluster tightly around 140.0 mmol/L; a larger SD means they are more scattered. SD says nothing by itself about whether that spread is acceptable: acceptability is a local-policy judgment applied to the number, not a property the number carries on its own.
Precision and low SD are related but not identical ideas. Precision describes variation among repeated measurements under defined conditions. A low SD on its own does not establish agreement with an assigned target; that comparison is a separate calculation, bias, covered in the next section.
State the dataset (control level, lot, method, analyzer, time window, and whether the process was stable) before quoting a mean or SD, because the same two numbers mean different things attached to different datasets.
Reading one run's descriptive statistics, in order
Define the dataset
Name the control level, lot, method, analyzer, operator, and time window before any calculation, and confirm the process was believed stable across that window.
Plot the results in time order
Look at the run as a sequence before summarizing it, so a shift, trend, or other structure is visible instead of hidden inside an average.
Compute the mean and SD
Calculate the arithmetic mean and the sample SD (n minus 1) for the defined dataset, keeping the result's unit attached to both numbers.
Compute CV and bias
Divide SD by the mean for CV, and subtract the assigned target from the mean for bias, so relative spread and target agreement are both visible.
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