Read pooled means in Book Isle: check group-size weights first

Adding two group means and dividing by two gives an equally weighted average of groups, not necessarily the mean across all people. Return to source table and sentence in Book Isle, then calculate a simple invented example in your own notes. This differs from percentage-denominator checking and does not turn the app into a spreadsheet or statistics package. Identify the averaging unit, weights and pooling conditions without judging real schools, incomes or studies.

Identify the averaging unit and source

Choose an accessible short discussion of means and record title, edition, chapter, table and referencing sentence. Ask whether it describes people, groups or measurements instead of treating every average as the same indicator. Retain quantity, unit, time window and inclusion scope, including off-page notes. If average does not specify arithmetic mean, median or another measure, mark unresolved rather than applying a formula. Search can locate a distinctive phrase without establishing calculation scope. Keep source wording separate from your question so later checks reveal whether the question changed.

Record group sizes beside their means

Invent group A with two people and arithmetic mean 10 exercise units per person, and group B with eight people and mean 20 of the same quantity. Assume disjoint groups, the same measurement/time window and equal contribution per person. Record group, count, mean and unit, not just 10 and 20. Counts are not the mean’s unit, and mean 10 is not total 10. If a source mixes median and mean, pooling by this method is unavailable. Do not zero-fill missing counts or guess equality. Clearly label invented values rather than presenting them as book data.

Recover group totals and then combine

A’s total is 2×10=20 and B’s 8×20=160. Combined total is 180 across 2+8=10 people, so pooled per-person mean is 180/10=18 units. Name quantities and units at every step rather than retaining only 18. Use your own calculator; Book Isle retains sources and notes without an assumed calculation sheet. A result of 180/2=90 confuses group count with people. Adding means to get 30 confuses means with totals. Mean and count must reconstruct the same summed quantity; estimated or rounded means may yield only approximate totals, a limitation retained later.

Explain why 15 answers a different question

(10+20)/2=15 gives each group half the weight: an equal-weight mean of group means, not the pooled per-person 18 here. Do not call 15 universally wrong; specify the target. The pooled mean is also 0.2×10+0.8×20=18, with weights 2/10 and 8/10 summing to 1. If both groups instead contain five people with unchanged means, pooled mean 15 is valid in that different invented case. Name original and variant separately rather than silently altering counts. Different answers then reflect weighting, not inconsistent calculators.

Check whether pooling is meaningful at all

Return to the table and check overlapping people, units, time windows and measurement definitions. Repeated records for one person differ from one per person; row count is not automatically people count. Proportions, rates and other indicators do not universally use head-count weights; inspect their denominators and question. Retain separate group values when incompatible instead of forcing one mean. Knowing the formula cannot supply missing data. Record confirmed and missing pooling conditions rather than treating tidy layout or matching labels as comparability.

Retain rounding and missing-value limits

Integer-displayed group means may reconstruct only approximate totals; calculator decimals do not become original precision. Missing counts prevent this recalculation, and missing means are not zero. Retain any source-defined weights instead of assuming one per person. Medians cannot reconstruct sums through this method, and pooled standard deviation is not simply a size-weighted mean of group SDs. Limit the first exercise to the mean and flag other statistics separately. Keep displayed and derived values distinct so later paraphrases do not attribute calculations directly to the author.

Check from table to note and back

Bookmark or externally locate table, mean definition and conclusion. Leave and reopen the reader and rematch 2, 8, 10 and 20 to their fields. Recalculate with the result hidden, then check 18 lies between 10 and 20: a positive-weight sanity check, not proof of correctness alone. Reopen exported notes and inspect multiplication signs, decimals, group labels and approximation marks. Plain text suffices without a formula editor. After revision, recheck headers and scope instead of equating table numbers. Explain corrections, distinguishing transcription errors from a mistaken averaging unit.

Finish with both question and weights

Explain what original pooled 18 and equal-group 15 answer, which conditions permit size weighting and which missing fields stop it. Retain table location, counts, means, recovered totals, combined count and one limitation, not just a formula screenshot. If the author asks for an equal-group mean, your separate 18 does not establish an error; align questions first. Recheck quantity and weights in the next source rather than treating this example as a universal shortcut for averages. The card verifies a selected example, not automatic analysis or trustworthiness of the whole source.

Related tutorials and sources

Read statistical claims in Book Isle: restore denominators, time windows and source tables; Book Isle data tables: distinguish zero, blank, dash and unspecified values.

Sources checked on 7 November 2026: the official Book Isle App Store listing and Apple Lookup 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: NIST weighted-mean definition. Only the weighted-sum divided by weight-sum concept is used. Counts, values and Book Isle records are invented; the source’s software commands are not required.