Descriptive statistics

Location says where the centre is. The mean is the best known and the most fragile: a single extreme value shifts it. The median, the value that cuts the sample in two, does not move — which is why salaries are given as a median and not a mean.

Spread says how far the values depart from that centre. The range, the difference between the maximum and the minimum, can be worked out in your head but retains only two points. The standard deviation measures the typical deviation of the whole set, and it is what feeds all the rest of Six Sigma — capability, control charts, tests.

Shape says how the values are distributed around the centre: symmetrical or skewed to one side, tight or spread out, with a single peak or several. Two peaks in a histogram are one of the most useful signals in Lean Six Sigma: they almost always betray two mixed populations — two machines, two shifts, two suppliers.

A histogram, a box plot or a simple scatter of points in chronological order teach more than three indicators. Data sets with identical means and standard deviations can look radically different; only the chart tells them apart.

Chronological order deserves a separate mention. Arranging the measurements in production order reveals drifts, jumps and cycles that any numerical summary erases — and a slow drift is exactly the kind of problem one never finds by looking at a monthly average.

One almost always measures a sample, and wants to conclude about the population. That passage is never free: two samples drawn from the same process will give two different means, and the gap between them is nothing abnormal.

Hence the caution to keep in front of two figures that differ: before seeing an effect, one has to know by how much they would have differed without anything happening. Comparing two means by eye leads to launching projects on noise — statistical tests exist precisely to settle that point.