Descriptive Statistics: Read Centre, Spread and Outliers Before You Test Anything

Descriptive Statistics summarises what your measurement actually looks like. It reports centre, variation, distribution shape and unusual values, either overall or broken down by group, and it keeps the uploaded data visible while it does so.

You use it early in the Analyse phase of RDMAICS. By that point you have a defined problem and a measurement you trust. Before you run a hypothesis test, build a control chart or argue about a cause, you need a plain description of the numbers in front of you.

The tool is also useful as a sanity check after measurement. If a group has a spread far wider than the others, or a value sitting a long way from its neighbours, you want to know that before any statistic is quoted in a steering meeting.

Reach for it whenever someone says an average out loud. An average on its own hides almost everything that matters.

The worked example below is fictional. It is the sample data built into the tool, and no real organisation, team or result is being described.

The dataset holds 24 observations. Each row is one observation or period, labelled A-01 through C-08. Each row carries a measurement to summarise, a group or stratum, and a series or scenario.

Three groups appear: Team A, Team B and Team C. Each has eight observations. Within each team, four observations sit in the Baseline series and four in the Pilot series. The measurements run from 27.4 at the low end to 58.9 at the high end.

That single value of 58.9 belongs to row 20, observation C-04, in Team C Baseline. Keep it in mind. It drives much of what the tool reports later.

The data table is the starting point. Four columns are mapped to four roles, and the tool names them plainly so you can match your own spreadsheet without guessing.

Observation or period holds the label. Measurement to summarise holds the numeric value, and it is the only required numeric field. Group or stratum holds the category you want to split by. Series or scenario holds a second label, here Baseline or Pilot.

Four settings then control the output. In this example, Summarise by is set to Group or stratum, so the tool produces one summary per team. Better performance means is set to No preferred direction, which tells the tool not to label high or low values as good. Box plot orientation is Horizontal. Fitted normal curve is switched on.

The No preferred direction setting matters more than it looks. With it selected, the tool describes without ranking. If higher or lower were genuinely better for your measure, you would say so here and read the output with that direction in mind.

The result panel opens with counts. 24 rows analysed. 3 summaries produced. 0 rows excluded for blank or non-numeric measurements. The overall mean is 35.35. One potential outlier is flagged under the Tukey 1.5 by IQR rule.

Zero exclusions is a small but useful signal. Every row carried a readable number, so nothing was quietly dropped. When that figure is not zero, you go back to the source data before reading anything else.

The tool also offers an AI review that explains the calculated result in words and marks the finding as descriptive rather than inferential. The wording is deliberate. Observed differences between groups are not the same as tested differences.

Four visuals follow the headline numbers: mean with 95 per cent confidence interval, a distribution histogram, a box plot comparison and a plot of every included measurement.

Team A has a mean of 29.6375 and a median of 29.45. Standard deviation is 1.7312, variance 2.9970 and CV 5.84 per cent. Values run from 27.4 to 32.5, a range of 5.1, with an IQR of 2.325. Skewness is 0.384 and no outliers are flagged. The 95 per cent confidence interval is 28.190 to 31.085.

Team B has a mean of 35.2000 and a median of 35.05. Standard deviation is 2.0826, variance 4.3371 and CV 5.92 per cent. Values run from 32.8 to 38.4, a range of 5.6, with an IQR of 3.325. Skewness is 0.289 and no outliers are flagged. The interval is 33.459 to 36.941.

Team C is the interesting one. The mean is 41.2250 but the median is 39.1000. Standard deviation is 7.6097 and variance is 57.9079. CV jumps to 18.46 per cent against roughly 5.9 per cent for the other two. The range is 23.1 against an IQR of 5.225. Skewness is 2.196 and one outlier is flagged.

That gap between mean and median, the inflated CV, the range of 23.1 and the skewness of 2.196 all point at the same thing. One value, 58.9, is pulling the average up. The box plot shows it as a separate red point above the Team C box, and the every-measurement plot shows the same gap.

The standard error of the mean tells a similar story. It is 0.6121 for Team A and 0.7363 for Team B, then 2.6904 for Team C. The confidence interval widens from roughly three units wide to 34.862 to 47.588.

The first decision is about the outlier. The tool flags 58.9 as a potential outlier under the Tukey rule. It does not tell you whether to remove it. Your job is to go back to observation C-04 and find out what happened during that period. A data entry error, a process event and a genuine extreme all look identical in a box plot.

The second decision is about where to look next. Team C carries most of the variation in this dataset. With a CV of 18.46 per cent against 5.84 and 5.92, a variation reduction effort has a clear starting point.

The third decision is about which statistic to quote. For Team A and Team B, mean and median sit close together, so either is reasonable. For Team C, the mean of 41.2250 and the median of 39.1000 tell different stories. Quote both, or quote the median and say why.

The fourth decision is what test to run. The confidence intervals for Team A and Team B do not visually overlap, but the tool states clearly that overlap, or the lack of it, does not by itself settle the question. An inferential test comes next.

The most common mistake is quoting the mean alone. In this dataset, Team C at 41.2250 sounds like a stable number. The standard deviation of 7.6097 says otherwise.

The second mistake is reading the fitted normal curve as a test. The tool labels it directly: the dashed curve is a visual reference, not a normality test. It is there to help your eye, nothing more.

The third mistake is treating the summary-by-group view as the only view. The histogram offers both an Overall and a Compare groups mode. Start overall, then split only when the question is genuinely about strata.

The fourth mistake is ignoring the series column. Here the Summarise by setting is Group or stratum, so Baseline and Pilot are pooled inside each team summary. The four Pilot values in every team sit lower than the four Baseline values. A summary by team alone will not surface that pattern.

Descriptive Statistics describes. It does not test. The result panel says so plainly, and so should you. Observed averages ranging from 29.64 in Team A to 41.23 in Team C is a description, not a finding of statistical significance. A separate inferential test is required before you use the word significant.

It will not tell you why Team C varies more. It will not tell you whether 58.9 is an error, an event or a real extreme. It flags the value under a fixed arithmetic rule and leaves the judgement with you.

It will not tell you whether higher is better. In this example the direction setting is No preferred direction, so nothing in the output ranks the teams by performance. Even with a direction set, the tool only orients the reading. It does not assign blame or credit.

It will not detect drift over time. With 24 observations, it gives you a snapshot. Stability and special cause behaviour belong to a control chart, not to a summary table. A dataset can show a tidy mean and a stable looking box plot while the process is trending steadily out of control.

Finally, it will not fix your measurement system. Zero rows excluded means every value was numeric. It does not mean every value was correct. If the measurement definition is loose, the summary will be precise and wrong. Confirm the measure first, then describe it.