Move one reading, move the mean
Five seed trays hold 20, 22, 24, 26 and 28 shoots. Shoots are young green stems. You recount the last tray. The last tray has ten more shoots than you wrote down. How does the mean change?
Loading lab…
- Five trays: 20, 22, 24, 26, 28. Mean 24.
- The fifth tray becomes 38. Mean moves to 26.
The move is shared out
The mean rises by 2, from 24 to 26. The move is how much one reading changes.
The five trays add to 120. Shared five ways, 120 ÷ 5 = 24. So the mean is 24. One tray gains 10, so the total is 120 + 10 = 130. Now 130 ÷ 5 = 26.
The reading moved 10. The mean moved from 24 to 26, which is 2. That is 10 shared among five trays: 10 ÷ 5 = 2.
This works when one reading changes and the count stays the same.
Rule: The mean moves by the move divided by the count.
Two scores are 30 and 50. They add to 80. Shared two ways, 80 ÷ 2 = 40. Change the 50 to 60. The move is 10. Shared two ways, 10 ÷ 2 = 5. So the mean goes from 40 to 45.