# Read median and mean with Book Isle: recompute after changing one large value

Language: en
Canonical: [Read median and mean with Book Isle: recompute after changing one large value](<https://allluckly.cn/en/guides/nasbook-median-mean-extreme-value-comparison/>)
中文：[中文 HTML](<https://allluckly.cn/guides/nasbook-median-mean-extreme-value-comparison/>)
English: [English HTML](<https://allluckly.cn/en/guides/nasbook-median-mean-extreme-value-comparison/>)
Published: 2026-11-09T00:00:00+08:00
Modified: 2026-11-09T09:37:10+08:00
Author: Bison

Use five invented minute values to compare ordered position and total, checking repeats, even counts and an extreme-value change.

English translation of the [Chinese original](<https://allluckly.cn/guides/nasbook-median-mean-extreme-value-comparison/>), translated on 2026-11-09. Original publication dates, attribution, code and version notes are retained.

An increased average reading time does not necessarily mean the middle-ranked session became longer. Median uses ordered position; arithmetic mean divides total by count. Both describe centre but are not interchangeable. Read a statistics text in Book Isle and preserve five original practice values in your notes, then recompute after changing one large value. The app neither detects extreme values nor selects the appropriate statistic automatically; check calculations, units and scope manually.

## Save the passage location and exact statistic name

Open a lawful text or reference, recording title, edition, chapter and example number with an available bookmark. Copy whether it says mean, median or an ambiguous average rather than silently substituting your preferred term. Distinguish printed/file pages in PDF; retain chapter and a short phrase for reflowable text instead of font-dependent page numbers. Verify example heading and context among multiple search hits. Manually record short names and locations if selection is unavailable; image excerpting is not guaranteed, and one hit does not establish a checked definition or scope.

## Retain five minute values with observation identities

The invented data consists of sessions A–E lasting 2,3,3,4,8 minutes, one value per session. Save A=2 through E=8 in original order and make a separate sorted copy rather than overwriting observations. Retain both B and C at three; deduplication would wrongly leave four. There are no missing values, weights or differing duration definitions, so all five count equally. Keep real data with such conditions separate instead of forcing this formula. These fictional values describe no actual users and must not be presented as an experiment performed through app timing statistics.

## Find the median position and then its value

Sort as 2,3,3,4,8. The third of five is central, with value three minutes. Position three and value three coincide here but must remain distinct; a median is not always its position number. Check two observations on each side, counting both repeated threes. Sort if you selected the middle unsorted row. Averaging endpoints two and eight to obtain five uses the wrong rule. The median need not be the most frequent value; three happens to repeat here, but that coincidence does not replace ordered-position reasoning with a mode claim.

## Calculate mean through both sum and count

The sum is 2+3+3+4+8=20 minutes; divide by five sessions for four minutes. Retain sum, count and unit to detect a missed repeat. Mean four differs from median three, yet both correctly describe different aspects of this dataset’s centre. If dividing by four, recount A–E. If calling twenty minutes the average, divide by session count. A mean need not equal an observed duration; four happens to appear here but is not required to. Keep calculation rules separate from individual observation identity.

## Change only eight to eighty and recompute

Save a variant retaining A–D as 2,3,3,4 and changing only E from eight to eighty minutes, still five sessions. Sum becomes ninety-two and mean 92/5=18.4 minutes. The third value of 2,3,3,4,80 remains three, so median stays three minutes. Record changed observation and fixed conditions first; eighty is not a sixth item. Revisit position rules for a median of 18.4 or the sum for a mean still four. This change affects the mean without moving the middle position; it does not establish that medians never change or that eighty must be a typo.

## Use both middle values for an even count

In a separate example append a ten-minute session to the original five, giving 2,3,3,4,8,10. The third/fourth values are three/four, so median is (3+4)/2=3.5 minutes, not a chosen third item or an average of position labels treated as data. Sum thirty gives mean five. Name this six-session example separately from the eighty-minute variant; 2,3,3,4,80,10 cannot inherit results 3.5 and five. Update position rules when count changes. A missing repeated three shifts later positions, so repair the list rather than only the final answer.

## Check a large value’s source rather than deleting it

For a large real value inspect unit, original table, decimal mark, duplicate entry and observation definition, marking confirmed or unresolved rather than deleting it because it moves the mean. Contrasting summaries alone proves neither error, distribution type nor a more honest statistic. Record the author’s rationale and data availability, labelling your interpretation separately. Do not fabricate sorted observations when full data is unavailable. Exit and reopen the same example to verify bookmark, edition and terminology; record location failures specifically instead of assuming notes guarantee traceability.

## Explain the statistic across three named versions

Save three separate records: original five, five with eighty, and six with ten added. Include sorted list, count, sum, mean, median and source location. Explain without the solution why four/three differ, why 18.4/three respond differently and why the six-item median averages two middle values. Repair position or sum fields if you only recall answers rather than adding terminology. Limit conclusions to invented practice, not universal reading habits. Start new data records with weights, missingness and units. Viewing progress does not establish correct statistics; independently reproducible notes do.

## Related tutorials and sources

[Read pooled means in Book Isle: check group-size weights first](<https://allluckly.cn/en/guides/nasbook-group-means-weighted-average/>); [Read statistical claims in Book Isle: restore denominators, time windows and source tables](<https://allluckly.cn/en/guides/nasbook-statistical-claim-denominator/>).

Sources checked on 9 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 measures of centre](<https://openstax.org/books/introductory-statistics-2e/pages/2-5-measures-of-the-center-of-the-data>) supplies mean and odd/even median definitions. All reading-minute values are original practice data, not actual user statistics.