Combine defect counts across unequal inspection batches

Two inspection batches have different sample sizes. Produce the overall defect rate and identify which batches cross a stated internal review trigger.

SOURCE DATA
"batch","inspected_units","defective_units"
"A","100","5"
"B","900","9"

RULES
Each inspected unit is counted once, and defective_units counts units rather than the number of defects.
Overall rate = total defective units ÷ total inspected units. Do not average batch percentages equally.
Flag a batch only when its own defect rate is greater than 2%. This is a fictional review trigger, not an acceptance sampling standard.

MY FIGURES
Total inspected units: __________
Pooled defect rate (%): __________
Inspected units without a defect: __________
Batches above the review trigger: __________

MY REVIEW NOTE
________________________

METHOD
A has a 5% defect rate and B has a 1% rate. Their sample sizes are 100 and 900 respectively.
Pool counts: 14 defective units out of 1000 inspected gives 1.4%. The unweighted average of 5% and 1% would be 3%.
Flag A for review. The overall rate is below 2%, but it does not erase the higher observed rate in that batch.

REFERENCE ANSWERS — try first
Total inspected units: 1000. 100 + 900 = 1000.
Pooled defect rate (%): 1.4. 14 / 1000 × 100 = 1.4%.
Inspected units without a defect: 986. 1000 − 14 = 986.
Batches above the review trigger: 1. A is above 2%; B is below it.

Counting defect occurrences instead of defective units can produce a rate above 100% and a different measure entirely. Keep the numerator definition explicit.

A small observed sample is not a production guarantee. Keep inspection scope, batch sizes and the review rule attached to the report.

Occupational context: O*NET 31.0 Database, USDOL/ETA, Task 39, occupation 11-3051.00. https://www.onetcenter.org/dl_files/database/db_31_0_csv/task_statements.csv
CC BY 4.0: https://creativecommons.org/licenses/by/4.0/
Original practice material and adaptations by Skill Workbench. USDOL/ETA has not approved, endorsed or tested these additions. O*NET is a trademark of USDOL/ETA.