KURT in ONLYOFFICE: Sample Excess Kurtosis with Reconstructed Moments

Create ShapeData. Put Duration in A1 and enter numeric values 1,2,3,4,10 in A2:A6, measured in minutes. These five observations are deliberately small enough to reconstruct the calculation; they are not a representative study or proof of a distributional model.

Their mean is 4. The deviations are −3,−2,−1,0,6. The sums of squared, cubed and fourth-power deviations are respectively 50,180,1394. In C1:E1 enter Squared, Cubed and Fourth. Put =(A2-AVERAGE($A$2:$A$6))^2, =(A2-AVERAGE($A$2:$A$6))^3 and =(A2-AVERAGE($A$2:$A$6))^4 in C2:E2 and fill through row 6. Summing each helper column reconstructs those totals.

Keep the original numeric values unchanged when adding controls. For typed-input tests, place the literal text note in H2, the logical value TRUE in H3, leave H4 genuinely empty, and put =1/0 in H5. These are different cell types, not four interchangeable missing-value markers. The expected source behavior of references can differ from literal arguments.

The official reference accepts numeric arguments or ranges. The tagged implementation uses a finite-sample adjustment and subtracts a correction associated with the normal-distribution reference. Zero is therefore the reference for normal excess kurtosis; the raw normal fourth standardized moment is 3, not 0.

Kurtosis reflects fourth-power deviations and is very sensitive to extreme values. Describing it only as the sharpness of a peak is misleading: tails and outliers strongly influence the statistic. A positive result from five observations does not prove that their generating distribution has heavy tails, and a negative result does not establish that extreme observations are impossible.

Let n be the numeric count, x̄ the mean, and s the sample standard deviation using divisor n−1. The implemented expression is:

n(n+1)/[(n−1)(n−2)(n−3)] × Σ((x−x̄)/s)^4
− 3(n−1)^2/[(n−2)(n−3)]

For the main data, n=5, s²=50/4=12.5 and s⁴=156.25. The fourth standardized sum is 1394/156.25=8.9216. The coefficient is 30/24=1.25; the subtraction is 8. Thus 1.25×8.9216−8=3.152.

The last two rows shift or positively rescale every observation. Standardized fourth moments do not change under these transformations. Negative rescaling also preserves kurtosis because the fourth power removes sign. Unlike skewness, kurtosis does not indicate which side has the longer tail.

For the five values, the unadjusted central-moment ratio is (1394/5)/(50/5)²=2.788. Its unadjusted excess is −0.212. Those differ substantially from the sample-adjusted result 3.152 because the sample is tiny. Do not compare a reported raw kurtosis or unadjusted excess directly with KURT without aligning definitions.

The adjustment is not a guarantee of a stable or unbiased estimate for every population. A single outlier can dominate the fourth powers. Inspect the raw observations and sample size, and avoid using one scalar as a normality test or a rule for deleting inconvenient data.

The inspected code takes numeric cells from ranges and references, skipping nonnumeric values there. Direct logical and empty arguments are converted to numbers, while direct strings are skipped. Thus =KURT(A2:A6,TRUE) is source-predicted to include an extra 1 and yield approximately 3.63931947069943; referencing H3 instead leaves the five-value result 3.152. Numeric text is not automatically the same as a numeric cell in these branches.

Range/reference error values are also skipped by this numeric-only collection path, whereas a direct error argument is propagated. This inconsistency can hide damaged inputs. It is a source observation, not a recommendation to rely on silent error omission; inspect H5 and the selected range before interpreting a result.

The local formula has no early guard for too few values or zero spread. With only three numeric values, or with four identical values, its divisions produce a nonfinite number that the numeric wrapper maps to #NUM!. Therefore =KURT(1,2,3) and =KURT(2,2,2,2) are source-predicted #NUM!, not a valid zero or an asserted cross-product #DIV/0! rule. Use at least four varying numeric observations, while remembering that this minimum is not a recommendation for statistical reliability.

Checked October 18, 2026 against current official help and SDKJS tag v10.0.0.169, commit 3679e0375a758d7dc59d31337a45461be3525ed8. Introduction dates and a final supported-version endpoint are not established. Desktop Editors, Docs, mobile releases and imported files require separate compatibility checks.

Neither the ONLYOFFICE application nor its calculation engine was executed for this guide. The numerical targets are independently calculated mathematical values; code-path and error observations are manual source traces. They are not screenshots, displayed workbook results or promises of identical final digits. Use English function names and comma separators as shown, adapting separators to the editor’s locale.

Keep inputs and intermediate probabilities numeric and unrounded. Format the display rather than replacing values with rounded strings. These moderate scalar examples do not certify extreme-tail accuracy, unusual type coercion, array entry or dynamic spill. Model assumptions must be checked separately from arithmetic correctness.

• Official KURT help, checked October 18, 2026.
• Pinned implementation.
• Shared skewness helper.
• Numeric wrapper and error conversion.
• SKEW.
• SKEW.P.
• TRIMMEAN.
• PROB.