Where do your values collect when their average looks ordinary? Histogram buckets show where observations collect and where the distribution has empty space.
Define the Population and Boundaries
A useful histogram begins with a clearly defined observation. This example counts one row per measured value. If your source contains repeated measurements, decide whether every measurement or each subject belongs in the population.
Ranges need an unambiguous boundary convention. Use an inclusive lower bound and an exclusive upper bound. A value at a shared boundary then belongs to exactly one adjacent bucket.
I write that convention beside the bucket definition. I also count missing and out-of-range values separately. Otherwise a tidy chart can quietly omit the records that need the most attention.
The synthetic sample below includes boundary values, a high value, and a missing value. These are selected inputs for the demonstration. They do not represent observed production data or a measured distribution.
CREATE TABLE #Measure
(
ObservationId int NOT NULL PRIMARY KEY,
MeasuredValue int NULL
);
INSERT #Measure VALUES
(1,0),(2,9),(3,10),(4,25),(5,35),(6,59),(7,99),(8,NULL);
DECLARE @Width int = 10;
IF @Width <= 0 THROW 50001, 'Bucket width must be positive.', 1;
SELECT MeasuredValue / @Width AS BucketNumber,
COUNT_BIG(*) AS ObservationCount
FROM #Measure
WHERE MeasuredValue >= 0 AND MeasuredValue < 100
GROUP BY MeasuredValue / @Width
ORDER BY BucketNumber;Use Integer Division for Nonnegative Values
Integer division gives a convenient fixed-width bucket number for nonnegative integers. Values zero through nine belong to bucket zero when width is ten. Value ten begins bucket one under this convention.
The filter makes the supported domain explicit. It excludes missing values and numbers outside zero through ninety-nine. A separate diagnostic must explain those excluded observations when the report covers the complete population.
Integer division truncates toward zero for negative values. That differs from flooring toward negative infinity. Use a deliberate FLOOR expression with suitable decimal arithmetic when the population includes negative measurements.
DECLARE @Width int = 10;
SELECT ObservationId, MeasuredValue,
FLOOR(CONVERT(decimal(19,4), MeasuredValue) / @Width) AS SignedBucketNumber
FROM #Measure
WHERE MeasuredValue IS NOT NULL;
SELECT COUNT_BIG(*) AS MissingValues
FROM #Measure WHERE MeasuredValue IS NULL;
SELECT ObservationId, MeasuredValue
FROM #Measure
WHERE MeasuredValue < 0 OR MeasuredValue >= 100;The grouped fixed-width query only returns occupied buckets. It does not invent rows for missing ranges. That distinction matters when empty intervals are part of the story readers need to see.
Do not use rounded division to assign boundary values. Rounding can move an observation into the neighboring bucket. The mathematical definition should match the labels that readers interpret.
Store Histogram Buckets as Explicit Ranges
A range table supports business-defined intervals and uneven bucket widths. Store the numeric bounds separately from the display label. Sorting by a stable bucket order avoids lexical label surprises.
The following ranges cover zero through ninety-nine without overlap. A value of one hundred is intentionally outside them. Each range satisfies its own lower-before-upper constraint.
CREATE TABLE #Bucket
(
BucketId int NOT NULL PRIMARY KEY,
LowerBound int NOT NULL,
UpperBound int NOT NULL,
BucketLabel varchar(30) NOT NULL,
CHECK (LowerBound < UpperBound)
);
INSERT #Bucket VALUES
(1,0,20,'0 to below 20'),
(2,20,40,'20 to below 40'),
(3,40,60,'40 to below 60'),
(4,60,80,'60 to below 80'),
(5,80,100,'80 to below 100');
IF EXISTS
(
SELECT 1
FROM #Bucket AS A
JOIN #Bucket AS B ON A.BucketId < B.BucketId
AND A.LowerBound < B.UpperBound
AND B.LowerBound < A.UpperBound
)
THROW 50002, 'Bucket ranges overlap.', 1;A row-level CHECK cannot detect overlap with another bucket row. The explicit overlap query performs that cross-row validation. Maintain an equivalent safeguard when ranges become editable application configuration.
Gaps deserve a separate decision too. They can be intentional exclusions or configuration errors. Compare the intended domain against the retained ranges before claiming complete coverage.
Preserve Empty Histogram Buckets with a LEFT JOIN
Start the aggregation from the bucket table rather than the measurements. LEFT JOIN retains each configured bucket when no observations match it. The ON clause applies the numeric boundary rule.
Count the matched nonnullable observation identifier. COUNT star would count the preserved outer-join row for an empty bucket. That would incorrectly report one observation where the correct count is zero.
SELECT B.BucketId, B.BucketLabel,
COUNT_BIG(M.ObservationId) AS ObservationCount
INTO #BucketCount
FROM #Bucket AS B
LEFT JOIN #Measure AS M
ON M.MeasuredValue >= B.LowerBound
AND M.MeasuredValue < B.UpperBound
GROUP BY B.BucketId, B.BucketLabel;
SELECT BucketId, BucketLabel, ObservationCount
FROM #BucketCount ORDER BY BucketId;
SELECT M.ObservationId, M.MeasuredValue
FROM #Measure AS M
WHERE M.MeasuredValue IS NOT NULL
AND NOT EXISTS
(
SELECT 1 FROM #Bucket AS B
WHERE M.MeasuredValue >= B.LowerBound
AND M.MeasuredValue < B.UpperBound
);Keep measurement filters in the ON clause when they belong to the matching population. Placing a right-side condition in WHERE can remove empty buckets. Review that placement whenever adding dates, categories, or other source restrictions.
The unmatched-value query exposes observations outside all configured ranges. Compare those rows with missing-value counts separately. A NULL measurement is a distinct category rather than an unusually low numeric value.
Add a Bounded Text Bar
REPLICATE provides a quick visual comparison inside query output. A scaled bar avoids producing one character for every row in a large bucket. Keep the exact count beside the bar so the visual remains interpretable.
The following display maps the largest count to forty characters. Other occupied buckets receive proportional rounded-up lengths. An all-empty population receives empty bars without division by zero.
WITH Scale AS
(
SELECT BucketId, BucketLabel, ObservationCount,
MAX(ObservationCount) OVER () AS LargestCount
FROM #BucketCount
)
SELECT BucketLabel, ObservationCount,
REPLICATE(CONVERT(varchar(max), '#'),
CASE WHEN LargestCount = 0 THEN 0
ELSE CONVERT(int, CEILING(40.0 * ObservationCount / LargestCount))
END) AS TextBar
FROM Scale
ORDER BY BucketId;The explicit varchar max input avoids REPLICATE's ordinary eight-thousand-byte return limit. The chosen display limit is still only forty characters. Large-value typing does not mean an unbounded display is desirable.
A text bar is a diagnostic aid rather than a publication chart. Its appearance depends on the output font and client. Use a proper chart when readers need axes, comparable scales, or exported presentation quality.
Choose Histogram Buckets That Answer the Question
Histogram buckets that are too wide hide meaningful clusters. Very narrow ranges can turn ordinary variation into distracting spikes. Compare several sensible widths while retaining the same population and boundary convention.
Unequal-width ranges also need careful interpretation. Raw counts favor wider intervals because those intervals cover more values. If comparing density, divide by range width and label that metric explicitly.
Can a reader tell where an exact boundary value belongs? Test that by reviewing the numeric range and its label together. Labels such as twenty to forty are ambiguous unless their endpoint convention is stated.
I use histogram buckets to reveal distribution before choosing a summary statistic. I keep coverage checks beside the aggregation. Even an empty bucket deserves its place at the table.
Reconcile bucket totals with the source population and excluded categories. Preserve the same filters when comparing periods. A distribution comparison is meaningful only when both sides describe compatible observations.
Validate the Aggregation before Sharing It
A business histogram is different from the optimizer's statistics histogram. This script counts your chosen observations using your chosen ranges. It does not expose or replace the optimizer's distribution metadata for estimating query cardinality.
For a large source, evaluate an index on the measured value alongside other required filters. Range matching can use different physical plans depending on table sizes. Inspect the actual plan and workload before promising an efficient join strategy.
Weighted observations require another explicit decision. Summing an associated weight describes something different from counting observation rows. Label that measure clearly so readers do not confuse total volume with the number of sampled records.
Finally, test an all-empty population and values exactly at every shared boundary. Confirm that empty buckets remain visible and each valid observation appears once. Those small checks protect the defining behavior more directly than inspecting a colorful result alone.
Related reading on this blog: Grouping Dates Into Buckets With DATE_BUCKET and Approximate Percentiles With APPROX_PERCENTILE_CONT.
A histogram is not an average with decoration, it is a counted distribution with explicit boundaries.
Published by Pinal Dave on SQLAuthority. More of my work at pinaldave.com.
