Lesson 5 of 11
Two groups, one true mean
Show on a big screenSeed trays grow shoots, young green stems. Four shade trays have a mean of 20 shoots. Six sun trays have a mean of 30. Is the mean of all ten trays 25?
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Step 1 of 2
- Pivot on 25, the halfway mark. Tips right.
- Pivot on 26, the true mean. Level.
Go back to the totals
No. The mean of all ten trays is 26, not 25. The true mean is the mean of all the trays together.
The total is the mean × the count. The shade trays hold 4 × 20 = 80 shoots. The sun trays hold 6 × 30 = 180 shoots. Together that is 80 + 180 = 260 shoots over 10 trays. Now 260 ÷ 10 = 26.
There are more sun trays than shade trays. So the mean is closer to 30 than to 20.
Rule: Two means average to the true mean when both counts match. Otherwise rebuild the totals.
Try the lab to finish this lesson.