Histograms — Bins, Curves, Spec Limits

Histograms — the shape of a columnOne numeric column, cut into bins: the typical value, the spread, the skew and the stragglers, visible before anyone computes a statistic. A histogram answers "what does this column look like?". The range of a numeric column is cut into bins and each bar shows how many values fall in its bin — so a long tail of large orders, a margin that clusters in two places, or a handful of fat-finger trades is visible at a glance. It needs one thing, the VALUE column; there is no category, because the x axis is the value itself. It is a chart type like any other: Dashboard → Add Widget → Histogram, Reports → Charts → Histogram on a sheet, or Histogram picked as any chart's type, with the same sources, formats, export buttons and PDF reports. Binning happens in the app, so dragging through bin rules is instant; for very large tables the counting moves into the database and only counts come back. Every screen in this chapter comes from the AnalyticsTable-Showcase project — the three histograms at the foot of its Forecast dashboard, and the same 10,000 orders drawn with each option in turn.

What it does

Bar height as the COUNT of values, the PERCENT of all values, the DENSITY (so bars of unequal width stay comparable) or the SUM OF ANOTHER COLUMN — a weighted histogram
Bin rules: Automatic (the finer of Sturges and Freedman–Diaconis), Sturges, Freedman–Diaconis, Scott, square root, Rice — or a number of bins, a bin width with an anchor, or your own edges
Round edges moves automatic edges onto 1, 2 or 5 × 10ⁿ so the axis reads 0–100 in tens rather than 3.2–97.8
A range of interest, From and To: values outside are counted in dashed "< from" and "≥ to" overflow bars, or left out entirely
Trim each tail drops up to 10 % of the lowest and highest values before binning, with a chip saying how many were left out
Curves at the same scale as the bars: a fitted normal curve, a kernel density curve, and a cumulative % line on its own 0–100 % axis
Markers at the mean, the median and any percentiles, and a shaded mean ± 1 standard deviation
Specification limits — LSL, USL and a target — tint the zones outside, colour out-of-spec bins and add Cp, Cpk and the out-of-spec share in percent and parts per million
Split by a category: overlaid, stacked or side by side, with percent and density worked out per group so a small desk and a large desk compare fairly
A statistics band under the chart: n, mean, median, standard deviation, minimum, maximum, interquartile range, skewness and kurtosis — and one line per group
Logarithmic bar height, horizontal bars, bin edges or centres on the axis
Where bins are counted: in the app (exact, up to the value limit) or in the database (counts per fine sub-bin, any size) — Automatic picks

How it works

Add the widget (Dashboard → Add Widget → Histogram), pick the table and the Value column. On a sheet, select a column of numbers before clicking Reports → Charts → Histogram and it is bound at once. Text cells that are not numbers and empty cells are left out, never counted as zero.
Bins include their lower edge and exclude the upper one, except the last bin, which includes the maximum. Changing the bin rule, the count or the width never re-runs the query.
A range of interest fixes the axis. With Values outside set to Count in "< from" / "≥ to" bars, the values outside gather in two dashed bars that read as overflow rather than bins; Leave out is a real filter applied before anything is counted, so the statistics describe only what is shown.
Curves and markers are drawn at the scale of the bars. With split groups each group gets its own curve in its own colour, and the statistics band adds a line per group.
On a dashboard the slicers and cross-filters apply before the values are counted, so filtering to one desk shows that desk's distribution. Clicking a bar filters the rest of the board to that bin's range of the value column — the chip reads, for example, "price ∈ 100 – 105" — and clicking it again clears it. A histogram never filters itself.
In the app, up to 100,000 values are fetched and binned exactly; a yellow chip warns if the limit cut the data off. In the database, only counts per sub-bin (1,000 by default) and exact sums come back, so a table of any size costs the same — the mean and standard deviation stay exact while the median, percentiles and density curve are accurate to one sub-bin and marked ≈.
The SQL is written for DuckDB, PostgreSQL, SQL Server, Oracle and BigQuery with forgiving casts, so a stray text cell becomes empty instead of failing the chart; every step appears on the Query Monitor, where it can be stopped.
CSV exports one row per bin — edges, label, count per group, total, measure and cumulative percent. Ask Greg can propose a histogram ("distribution of trade sizes by desk with the 5th and 95th percentile") and certifies it by the number of values it counts.

Practices that keep it reliable

Start on Automatic bins, then set a range of interest — one extreme value should not decide what the other 9,999 look like
Use density, not count, whenever bins are of unequal width; otherwise a wide bin looks important just for being wide
Compare groups of different size with overlaid percent, not counts — the Showcase's channels differ by a factor of two in orders
Trim tails to look at the body of a distribution, but keep the chip visible: the values left out are often the story
Put specification limits on anything with a tolerance — a price band, a margin floor, a settlement time — and read Cpk, not just the picture
On large tables leave Where bins are counted on Automatic; force In the database only when the value limit is being hit routinely

In a regulated environment

Specification limits turn a chart into evidence: Cp, Cpk and the out-of-spec share in ppm are computed from the same rows the chart draws and travel with it into the PDF pack.
Counting in the database means no row-level data leaves the source for very large tables — only counts per sub-bin and exact sums are returned.
Every histogram is a saved, diff-able definition in the project file; a changed bin rule or limit shows up in review like any other change.
Tail trimming and left-out ranges are announced on the chart, so a distribution can never be quietly cleaned before it is shown.

Every option, on a real screen

Automatic bins — the first look (Properties → Bins → Bin rule). Automatic uses the finer of Sturges and Freedman–Diaconis, which is what most statistics tools do. On order revenue it shows the honest picture: most orders under €2,000, a tail that runs past €30,000. The median (€1,176) sits far left of the mean (€2,120) — skewness 4.49 says the same in one number.
A fixed number of bins on a logarithmic axis (Properties → Bins → Bin rule). When counts span orders of magnitude, the tail disappears into the axis. Logarithmic bar height brings the one-order bins back into view — here 40 bins, from thousands of small orders down to single large ones.
Your own edges, read as density (Properties → Bins → Edges). Custom edges cut the axis where the business cuts it — price bands, trade-size tiers. Bins of unequal width need DENSITY as the bar height (count ÷ total ÷ width), so a wide band is not mistaken for a busy one; the area of all bars adds up to one.
A range of interest with overflow bars and percentiles (Properties → Range and outliers). From and To fix the axis to the part of the range worth reading. The orders above €6,000 are not dropped — they gather in a dashed overflow bar at the right edge — and the 5th and 95th percentile markers show where the middle 90 % lies.
Trim each tail (Properties → Range and outliers → Trim each tail (%)). Trimming drops the lowest and highest share of values before binning — the robust way to keep one fat-finger trade from flattening the picture. The statistics are computed on what is left, and a chip in the header says how many values went.
A density curve and the cumulative share (Properties → Curves and markers). The density curve (a Gaussian kernel estimate, Silverman's bandwidth unless you type one) smooths the bars into a shape; the cumulative % line on its own 0–100 % axis reads off questions such as "what share of orders earn under 20 %?".
Specification limits — a capability chart (Properties → Specification limits). Set a lower limit, an upper limit and a target and the chart becomes a capability chart: the zones outside are tinted, bins outside are coloured, and the statistics add Cp, Cpk and the share out of spec. It works as well for a margin corridor or a price tolerance as for a production line.
Split by region, stacked (Properties → Distribution → Split by). Split by draws one distribution per value of a category column. Stacked bars add up to the whole, so the outline is the overall distribution and the colours show who makes it up; the statistics band adds n, mean, median and σ per region.
Split by channel, overlaid, as a percent of each (Properties → Distribution → Bar height). Overlaid groups compare shapes. With Percent of values (or Density) each group is measured against its own total, so Online's 4,537 orders and Partner's 2,250 compare fairly. Here it shows what a table of averages would not: Partner margins sit a whole band lower.
A weighted histogram — the sum of another column (Properties → Distribution → Bar height). Sum of a column (weighted) turns counts into money: each bar adds up the chosen column for the rows in its bin. Binned by margin and summed by revenue, it answers "how much revenue do we earn at each margin level?" — notional by price band is the trading-desk version of the same chart.
Horizontal bars for small whole numbers (Properties → Bars and colours → Orientation). Units per order are small integers; a bin width of 1 anchored at 0.5 puts each whole number in a bar of its own, and horizontal bars give the labels room. The median (3) and the mean (4) are marked.
Counted in the database (Properties → Performance → Where bins are counted). In the database, the engine returns only counts per fine sub-bin and exact sums, so a table of a hundred million rows costs the same as this one. The "Binned in database" chip says where the work happened; the median and percentiles carry ≈ because they are accurate to one sub-bin, while the mean and σ stay exact.

Screens

Order revenue on the Showcase's Forecast dashboard — 250-wide bins from 0 to 10,000, mean, median and the 90th percentile marked.
Margin per order — a fitted normal curve, mean ± 1σ shaded and a 25 % target line.
Properties, top half — Distribution (value, bar height, split by), Bins, and Curves and markers.
Properties, bottom half — Specification limits and statistics, Prefilter, Bars and colours, and Performance.
Dashboard → Add Widget — Histogram and Forecast sit beside Chart, Heatmap and Waterfall.

Glossary terms on this page

KPI dashboard: definition

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