A frequency table can misclassify observations through its labels even when the formula is correct. Before building a chart, write the intervals precisely. “Below 10” and “10 or below” differ for a value of exactly 10, and an omitted overflow group can make records appear to vanish.

In a disposable Numbers table, put the numeric values 0, 5, 10, 10.1, 20 and 21 in A2:A7. Put the boundaries 10 and 20 in B2:B3. Keep them as numbers of the same kind rather than mixing quantities, dates and duration values.

FREQUENCY(data-values, interval-values) returns an array. Its first count includes values at or below the lowest boundary. Subsequent interval counts include values above the preceding boundary and at or below the current one. The final count includes values above the largest boundary.

Read each result explicitly

Apple documents using INDEX to retrieve an individual result from FREQUENCY. Enter =INDEX(FREQUENCY(A2:A7,B2:B3),1) in a separate output cell. In two more output cells, use the same formula with the final 1 changed to 2 and 3. These positions retrieve the three counts, including overflow.

The expected results are 3, 2 and 1. The first group contains 0, 5 and 10; the second contains 10.1 and 20; the final group contains 21. Add the counts independently: all six input observations are accounted for.

Label the outputs “10 or below”, “Above 10 through 20” and “Above 20”. Those labels communicate the inclusive and exclusive boundaries without asking a reader to infer them from a vague range such as 10–20.

Test the boundary before using real observations

Temporarily change 10 to 10.1 in the practice data. The first count should decrease to 2 and the second increase to 3, while overflow stays 1. Restore the value after confirming the expected shift.

For a real distribution, decide the cutoffs according to the reporting purpose and retain the overflow output. Compare the sum of all counts with the eligible input count and investigate a mismatch. Keep the raw observations so changing a reporting boundary does not require reconstructing the data. These formula examples use commas; enter separators appropriate to your Numbers locale when required.

Reference: Apple: FREQUENCY interval rules.

Additional reference: Apple: INDEX reading an array result.