Apple Numbers STDEVPA: Population Standard Deviation with Mixed Values

• Introduced: Original release and introduction date are not established by the checked references.
• Availability: Currently documented in Apple’s Functions Help 15.4 documentation edition; no final supported-version endpoint is established.
• Scope: Shared iWork reference. Function-specific historical availability across Mac, iPad, iPhone and iCloud is unverified.
• Checked: October 14, 2026, against the official STDEVPA reference. Independent typed-data and mathematical checks; no native Numbers test.

=STDEVPA(value, value…)

The first value or collection is required; further values or collections are optional. Apple specifies at least two values, including for the population functions. One range argument can contain multiple values. Do not confuse the number of arguments with the number of included observations.

Text is allowed in a referenced cell but is not allowed as a directly entered string argument. For example, put pending in a cell instead of constructing =STDEVPA(4,6,"pending"). The latter is outside the documented argument contract; this guide does not assign it an unverified error token.

Apple specifically says dates or durations mixed with text or Boolean values produce an error. These examples do not establish homogeneous date/duration behavior.

Use STDEVPA when the included values represent the whole population you mean to describe. STDEVA uses the sample definition. Deciding which observations belong in that population is separate from choosing a formula.

Create a Numbers table named MixedDispersion, with eight columns A:H and ten rows, including one header row. Use Input, Type, Mapped value and Squared deviation as A1:D1. Enter:

Enter pending without quote characters. Leave A7 and C7 truly empty, rather than typing the instruction or a formula that returns empty text. The five numbers in C2:C6 are a manual reconstruction, not a claim that a pending measurement really equals zero.

In E2 enter =AVERAGEA(C2:C6) for 2.2. In D2 enter =(C2-$E$2)^2, and fill down through D6. The five squared deviations are 3.24, 14.44, 4.84, 1.44 and 4.84. Put =SUM(D2:D6) in E3 for 28.8.

Use G2:G6 for the results:

The reconstruction uses five included values, so its denominator is 5, or n. The square root puts the result back in the same units as the mapped numbers. G5 deliberately selects only the two original numbers, 4 and 6, to show a different data-selection policy. It does not silently treat all five mapped entries as measurements.

The printed decimals are rounded expected outputs. Keep unrounded formulas for later calculations; a display rounded to a few places should not become a replacement input.

Create SensorExample, with six columns and nine rows. In A1:C1 enter Day, High and Low. Use the following complete source data; enter the day labels as plain text and n/a as ordinary text without quotes, not a spreadsheet error value.

In E2 enter =STDEVPA(B2:B8) for approximately 29.4472894702. In E3 enter =STDEVP(B2:B8) for approximately 10.6092203086. These reproduce Apple’s stated comparison: the A-function includes the text marker as a seventh, zero-valued observation; the numeric-only calculation uses six recorded highs.

A missing temperature is not a measured 0 °F. The larger mixed-input result reflects that chosen conversion. Although the source example calls these days a sample, STDEVPA remains the population formula. Treating the listed observations as the complete population is a modeling choice, not evidence that a few days represent the wider climate.

Create FlagPopulation, with five columns and seven rows. Enter =TRUE() in A2:A4 and =FALSE() in A5. In B2:B5 enter the numeric reconstruction 1,1,1,0. Treat these four supplied flags as the complete set to describe.

For zero/one values with a fraction p of ones, population variance is p×(1−p). Three true flags out of four give 0.75×0.25 = 0.1875; taking its square root gives D4. The sample calculation uses the same squared deviations but a divisor of three instead of four.

Copy the table to AllTrueFlags and replace A5 with =TRUE() and B5 with 1. D2 becomes 1, D3:D6 become 0. An all-true collection has no variation, just as an all-false collection would. Low standard deviation therefore does not establish that a required check passed; look at the flag values or their mean as well.

Create ZeroControl, with three columns and six rows. Enter numeric 0 in A2:A3, text pending in A4 and =FALSE() in A5. Put =STDEVPA(A2:A5) in C2 and =STDEVP(A2:A3) in C3; both return 0. Text and a Boolean are present even though the dispersions match.

A difference between an A-function and a numeric-only calculation can reveal an inclusion-policy difference, as in the sensor example. Equality does not prove that every input is numeric, complete or valid. Inspect types and collection rules before interpreting the statistic.

Empty cells, text markers, numeric zeros and error cells are distinct inputs. The checked references do not establish every imported numeric-string representation, formula-produced empty string, native error label or numerical limit. Keep those cases separate from the explicitly typed examples above.

STDEVP explains the corresponding numeric-only statistic. STDEVA uses the other denominator choice. AVERAGEA explains the mapped mean, and SQRT connects variance to standard deviation.