Center

"I'm telling you, the typical player gets, like, thirty gems," Leo said. He puffed out his chest. "No way!" Maya shot back. "I only got eight! You're just saying that because you got that one lucky treasure chest."

Leo had found a mega-chest. It gave him 150 gems. The rest of us had much smaller piles. My pile had seven. Maya’s had eight. Sam’s had ten.

Center hovered over our table. "A perfect problem," they buzzed happily. "You are asking 'what's typical?' You are looking for the middle."

Center pointed a fuzzy leg at Leo. "You are using the mean. That's one way to find a middle."

"The mean?" I asked.

"It's what most people call the average," Center explained. "You add up all the numbers. Then you divide by how many numbers you have."

We grabbed a pencil. My 7 gems. Maya's 8 gems. Sam's 10 gems. And Leo's 150 gems.

We added them up. It came to 175. There were four of us. So we divided 175 by 4. The answer was 43.75.

"See!" Leo shouted. "The average is almost 44 gems! I told you!"

But Maya crossed her arms. "That's not right. Three of us got around ten. Your giant number is messing everything up."

"Exactly," Center hummed. "Your one big number is an outlier. It's a piece of data that's way different from the others. The mean is sensitive. An outlier can pull it way up, or way down. It gives you a middle that doesn't feel very middling at all."

This made sense. The "average" of 44 didn't describe any of us.

"So what do we do?" Sam asked.

"We try a different middle," Center said. "Let's find the median."

Center had us write our scores on four separate cards. 7, 8, 10, 150. "Now, line them up. Smallest to largest." We arranged the cards on the floor. 7 ... 8 ... 10 ... 150.

"The median is the number that's physically in the middle of the line," Center said. "When you have an even number of cards, like you do, you look at the two in the middle."

We looked. The two middle cards were 8 and 10.

"Find the number that's halfway between them," Center instructed. Halfway between 8 and 10 was 9. "Your median is 9," Center buzzed.

Maya, Sam, and I all nodded. Nine felt much more typical. It was close to what we had all gotten. Leo's crazy-high score didn't wreck it.

"The median doesn't care about outliers," Center said. "It just cares about what's in the middle of the line. It's a good, honest middle when your data is skewed, or lopsided."

"Okay, so that's two middles," I said. "You said there were three."

"The last one is the mode," Center said, their antennae twitching. "The mode is the number that shows up most often."

Sam pointed at our cards. "But none of our numbers show up more than once."

"A fine observation!" Center buzzed. "For this set of data, there is no mode. But what if these were the scores?"