Average & Dispersion: Replicate Statistics

Use it to summarize comparable replicates of the same quantity: masses, volumes, times or concentrations, expressed in the same unit. The sum gives a total when the quantities are additive; minimum and maximum locate the extreme measurements. The bubble accompanies work in other tools. To explore the distribution with histograms, quartiles or box plots, open Descriptive Statistics; for confidence intervals and hypothesis tests, use Statistical Inference.

The mean is the sum divided by the number of values. Sample standard deviation s uses the divisor n−1 and describes the spread of measurements; it is neither the standard error of the mean nor a confidence interval. CV is expressed as 100·s/|x̄|. It has a useful relative interpretation only on scales with a meaningful zero, such as mass or temperature in kelvin, rather than degrees Celsius. It is highly sensitive near a zero mean, and no universal 5% threshold guarantees good precision. A negative mean is accompanied by a note explaining the use of its absolute value.

Empty cells are omitted; an invalid nonempty entry pauses the summary until corrected. Up to 1000 measurements are accepted, with decimal points or commas and scientific notation. Paste accepts one column without a header, separated by line breaks or semicolons; commas are not data separators and thousands separators are not accepted. One value gives mean, count, sum and extrema; s and CV require two. CV is undefined when the mean is zero. Results outside the numerical calculation range are shown as — with a notice. Extreme values do not imply an erroneous observation and are never removed automatically.

• Three measurements: 10.0, 10.2 and 10.4n = 3 · x̄ = 10.2 · s = 0.2 · CV ≈ 1.961 % · sum = 30.6 · minimum = 10 · maximum = 10.4
• Two measurements: −1 and 1n = 2 · x̄ = 0 · s ≈ 1.414 · sum = 0 · minimum = −1 · maximum = 1 · CV undefined