HARMEAN in WPS Spreadsheet: Harmonic Means for Positive Rates

• Introduced: documented by 2019-06-17 in the official WPS lesson; original introduction is not established.
• Availability: WPS Office for Windows Personal; no numeric release is stated in the edition metadata.
• Scope: exact current supported builds remain unverified. The Windows lesson does not establish equivalent availability in other WPS clients.
• Checked: October 14, 2026 against function-specific documentation. Examples were independently calculated; no native WPS test was performed.

=HARMEAN(number1, [number2], ...)

Provide positive observations directly or through a range, name or array. The 2019 Windows Personal lesson describes 1–30 arguments; that historical maximum is not certified across every current build. Square brackets indicate optional arguments and are not typed.

The lesson documents #NUM! if any included data point is zero or negative. In a referenced range, text, logical values and genuinely empty cells are ignored, while zero remains an included numeric value and therefore triggers the stated domain error.

Examples use English function names, comma separators and explicitly numeric cells. No native WPS run was performed; displayed results are independently calculated expectations.

Enter 30 and 60 in A2:A3. In B2 enter =1/A2 and fill to B3:

=HARMEAN(A2:A3)
=1/AVERAGE(B2:B3)

Both have expected result 40. The reciprocals are 1/30 and 1/60; their mean is 1/40. Keep the reciprocal cells at full stored precision rather than rounding them before the final calculation.

The ordinary arithmetic mean of 30 and 60 is 45. The difference is mathematical, not a formatting discrepancy.

A journey has two segments, each 60 km, travelled at 30 km/h and 60 km/h. Segment times are 2 hours and 1 hour. The overall average speed is:

=(60+60)/(60/30+60/60)
=HARMEAN(30,60)

Expected result from both formulas: 40 km/h. Equal distances make each reciprocal speed contribute an equal distance weight to total travel time.

If the speeds instead apply for one hour each, total distance is 90 km over two hours and the correct average is 45 km/h. Equal time calls for the arithmetic mean in this two-segment model. Do not choose HARMEAN solely because the inputs are labelled speeds.

For 30 km at 30 km/h followed by 90 km at 60 km/h:

=(30+90)/(30/30+90/60)

Expected result: 48 km/h, from 120 km divided by 2.5 hours. Unweighted =HARMEAN(30,60) remains 40 and answers a different question.

Use actual totals and time contributions when distances differ. HARMEAN itself does not accept a separate weight argument, and repeating a value to imitate a weight needs its own justified counting model.

Enter numeric 30, numeric 60, text ‘90, =TRUE() and a genuinely empty cell in D2:D6:

=HARMEAN(D2:D6)

Expected result: 40, using only 30 and 60 under the documented referenced-type rule. Converting the text 90 into a real number produces three positive observations:

=HARMEAN(30,60,90)

Expected result: 540/11, approximately 49.090909091. The new value participates in both the reciprocal total and the observation count.

Replacing the blank with numeric zero instead creates the documented #NUM! condition. A zero cannot be discarded merely because the range also contains valid positive values. A negative numeric input likewise violates the domain.

=HARMEAN(4,4)
=HARMEAN(40,80)
=HARMEAN(400,800)

Expected results are 4, approximately 53.333333333, and approximately 533.333333333. Multiplying every positive observation by ten multiplies the harmonic mean by ten.

For positive observations, the harmonic mean is no greater than the geometric or arithmetic mean; all three are equal when every observation is the same. The WPS lesson’s statement that the inequalities are always strict is too strong. The equal-input control above demonstrates the missing equality case mathematically.

For the original pair 30 and 60, the harmonic mean 40 lies between the minimum 30 and maximum 60. This is a useful ordinary positive-input sanity check, not a complete native precision or overflow guarantee.

Investigate a nonpositive rate rather than converting every error to zero with a fallback. A missing or invalid measurement may require a different inclusion policy, and silently excluding it can change the population being summarized.

The source does not certify every direct text, Boolean, empty-dataset or imported-error conversion case. Keep those questions separate from the documented positive-number calculation. AVERAGE is the arithmetic alternative; it is not interchangeable without examining what is held equal in the model.

• WPS Academy: HARMEAN lesson, 2019-06-17 (Chinese; Windows Personal scope).
• Editorial testing standards.

Worked outputs are independently calculated expectations, not captured native results. The dated source establishes the stated product scope, not every current client or build.