Finding the Average — Mean of a Data Set

The Story

Ms. Rao wrote five spelling scores on the board: 8, 6, 10, 7, 9. "If I wanted one single number that fairly represents this whole group, what would it be?"

Kabir guessed the highest. "10?" "That only describes the best score, not the group," said Ms. Rao.

Anaya thought of it differently. "What if we imagine sharing all the points equally, like sharing sweets?"

"That's exactly the idea," said Ms. Rao. "First, add every score together." Anaya added: 8 + 6 + 10 + 7 + 9 = 40.

"Now share that total equally among however many scores there were." There were 5 scores. "40 divided by 5 is 8."

"That number — 8 — is the MEAN, often just called the average. It's what every score would be if the total were shared out perfectly evenly."

Kabir checked it made sense. "8 is between the lowest, 6, and the highest, 10. That feels right."

"Good instinct — the mean is always somewhere between the lowest and highest value, never outside that range," said Ms. Rao. "If your answer comes out bigger than every value, or smaller than every value, you've made a mistake."

She then gave a trickier set: the number of books read by 4 students in a month: 2, 3, 3, 20. "Find the mean."

Anaya added: 2 + 3 + 3 + 20 = 28. Divided by 4 students: 28 ÷ 4 = 7.

"Seven? But three of the four students read way fewer than 7 books," said Kabir.

"That's a real and important lesson," said Ms. Rao. "One unusually large value — like that student who read 20 books — can pull the mean up higher than most of the group. The mean is a useful single number, but it doesn't always represent every individual fairly when one value is very different from the rest."