# Read cumulative frequency with Book Isle: subtract adjacent totals to recover class counts

Language: en
Canonical: [Read cumulative frequency with Book Isle: subtract adjacent totals to recover class counts](<https://allluckly.cn/en/guides/nasbook-cumulative-frequency-difference-boundaries/>)
中文：[中文 HTML](<https://allluckly.cn/guides/nasbook-cumulative-frequency-difference-boundaries/>)
English: [English HTML](<https://allluckly.cn/en/guides/nasbook-cumulative-frequency-difference-boundaries/>)
Published: 2026-11-10T00:00:00+08:00
Modified: 2026-11-10T09:39:21+08:00
Author: Bison

Use cumulative totals two, seven and nine to check endpoints, sample size and relative frequency without summing cumulative entries.

English translation of the [Chinese original](<https://allluckly.cn/guides/nasbook-cumulative-frequency-difference-boundaries/>), translated on 2026-11-10. Original publication dates, attribution, code and version notes are retained.

Seven sessions up to ten minutes does not mean seven sessions in the five-to-ten-minute class: shorter observations are already included. Read a statistics source in Book Isle, recording thresholds, cumulative totals and class counts separately. The original example specifies nine fictional sessions, all no longer than fifteen minutes. Subtract with explicit endpoints, then check proportions. The app does not recover raw observations or interpret charts automatically; readers verify calculations and conclusions manually.

## Identify the table and cumulative direction

Open a lawful text and record title, edition, chapter, table number and column headings with an available bookmark. Determine whether cumulative means no greater than a threshold or no less than one; subtraction direction differs. Distinguish PDF file/printed pages and retain caption phrases for reflowable text. Manually transcribe image-only headings/thresholds and verify them. A search hit for cumulative may be elsewhere. Confirm units, scope and missingness in headings/notes, leaving unknown definitions unresolved rather than inferring them solely from increasing numbers.

## Specify nine sessions and three upper thresholds

The invented data has nine sessions with 0\<t≤15 minutes and no missing records. Write C(5)=2, C(10)=7 and C(15)=9, where C counts sessions no longer than its minute threshold. Retain thresholds and minute units; seven is a count, not seven minutes. The last cumulative count equals sample size only because all sessions are explicitly within fifteen minutes. A real truncated table may not reach the full sample. Keep invented conditions separate from app reading statistics and do not combine cumulative rows from different dates or populations.

## Check the first class against zero cumulative count

Since all durations are positive, C(0)=0. Class 0\<t≤5 has C(5)−C(0)=2−0=2 sessions. Five belongs here and zero is excluded; record both boundaries rather than vague under-five wording. A real table including zero needs its own definition. Strictly below five differs from no greater than five. Verify unclear inequality marks in the original instead of guessing. First cumulative equals first class here because the starting condition is explicit, not a universal shortcut.

## Subtract for the middle class with explicit endpoints

Class 5\<t≤10 has C(10)−C(5)=7−2=5 sessions. Seven includes the first two, so it is not the class count. Exactly five is subtracted and exactly ten retained. Writing 5≤t≤10 would conflict with this calculation; repair the boundary wording. Retain both source rows and subtraction order, identifying the resulting five as a count rather than threshold. For cumulative counts of values no greater than the threshold, subtract the smaller-threshold total from the larger-threshold total. A negative five signals reversed order; absolute value is not a repair.

## Check the last class and overall total

The last class 10\<t≤15 contains 9−7=2. Counts 2,5,2 sum to nine, matching both the premise and C(15). Summing 2+7+9=18 repeatedly counts earlier classes. Verify nonoverlap and complete coverage, not a coincidentally correct sum. Including a threshold in both adjacent classes duplicates boundary observations. Endpoint and total checks are separate. This example excludes durations above fifteen; do not invent an extra trailing class for a real table and fill zero without evidence about its coverage.

## Do not read cumulative seven as seventy percent

With denominator nine, cumulative relative frequency up to ten is 7/9≈77.8%, while the middle class is 5/9≈55.6%. Write exact fractions and rounding explicitly; count seven is not seventy percent. A new population denominator requires its own identity rather than reusing nine. Rounded class percentages may miss one hundred slightly; check exact fractions instead of altering a class to force the total. Without a known sample size, retain differences and leave percentages unresolved. A partial-range final cumulative count is not automatically the denominator.

## Distinguish increase, flat totals and missing entries

Upper-threshold cumulative counts for one population cannot decrease. A flat step may indicate zero class frequency, but blank is not automatically flat or zero. Investigate population/time changes or transcription if seven falls to six rather than prettifying the curve. Cumulative data recovers class counts, not unique individual durations; do not invent raw observations. Exit and reopen the table to verify headings/notes and record version differences or unresolved items. A bookmark is a return aid, not statistical validation. Identify the exact row/threshold rather than vaguely blaming app display.

## Explain cumulative and class counts through three fields

Save thresholds, cumulative totals and class differences with location, units, sample size and endpoint convention. Explain why up-to-ten is seven but the middle class five, and why cumulative entries cannot be summed as sample size. Repair endpoint/source-row reasoning if you merely recall 2,5,2 rather than adding terminology. Start a fresh record per table with direction and denominator identity. Reading completion does not establish correct arithmetic. Another reader should reproduce each difference; no real user sampling, automatic analysis or exhaustive chart recognition test occurred.

## Related tutorials and sources

[Read statistical claims in Book Isle: restore denominators, time windows and source tables](<https://allluckly.cn/en/guides/nasbook-statistical-claim-denominator/>); [Book Isle: Align interval brackets, inequalities and number-line endpoints](<https://allluckly.cn/en/guides/nasbook-interval-endpoint-number-line/>).

Sources checked on 10 November 2026: the [official Book Isle App Store listing](<https://apps.apple.com/cn/app/id6766198898>) and [Apple Lookup](<https://itunes.apple.com/lookup?id=6766198898&country=cn>) show version 1.1.4, requiring iOS / iPadOS 15.6 or later. This workflow uses local reading, search, bookmarks and notes for manual checking. Readers record the samples and conclusions; automatic chart recognition, statistical testing or proof verification is not assumed. Confirm available controls against the installed version and file type. The exercise does not claim step-by-step device testing in this batch.

Method reference: [OpenStax on frequency tables](<https://openstax.org/books/introductory-statistics-2e/pages/1-3-frequency-frequency-tables-and-levels-of-measurement>) supplies frequency and cumulative-relative-frequency concepts. Nine sessions and totals two/seven/nine are original practice conditions.