Tally and Display

Tally tilted her head and pulled out a fresh tally-sheet. "Show me," she said.

Pip flipped to the first page.

Tally read the journal carefully. She did not interrupt. She held her clean tally-sheet ready.

When she had read all forty-two days, she said: "Pip. You have really good data. You wrote down every day. You wrote down the slope. You wrote down the number. This is the kind of journal a real scientist would keep."

Pip blushed under his fur. "But I can't tell what it means."

"That's because you haven't counted the right things yet," Tally said. "Right now you have forty-two separate numbers. You need to bundle them. Each slope gets one column. Each acorn gets a tick mark. Let me show you."

She drew a fresh tally-sheet. She labeled the left column North. She labeled the right column South. She went through the journal day by day, making four-tick groups with a slash across:

For the north slope:

|||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| ||||

For the south slope:

|||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| |||| ||||

She counted at the bottom. North: 65. South: 75.

Pip's eyes went wide. "South wins."

"South has more. It wins on raw count. But hold on, Pip. Hold on."

Tally pointed at the journal again. "I noticed something while I was counting. You went to the north slope on odd days. Day 1, 3, 5, 7. You went to the south slope on even days. Day 2, 4, 6, 8. That means you went to each slope the same number of times. Twenty-one days at each."

"Yes," Pip said. "I wanted to be fair."

"That's exactly why I can compare the totals," Tally said. "If you'd gone to south fifteen times and north five times, the south's higher total wouldn't mean anything — you'd have just gone there more. But you went the same number of times. So the totals do mean something. South really is better."

Pip nodded slowly.

"But not by much," Tally added. "Seventy-five versus sixty-five. Ten acorns over forty-two days. That's less than a quarter of an acorn difference per day. Is that worth changing where you gather?"

Pip frowned. He did not know.

"That's where you call Display," Tally said. "I count. He shows. He'll know what to do."

She tilted her head up to the sky. A small monarch butterfly was already drifting down from a higher branch. She had been waiting for the call.

Display landed on the journal next to Tally. He folded his wings carefully. He took a long look at Tally's two columns.

"Sixty-five," he said. "Seventy-five. Forty-two days."

"Yes."

"And the totals are the bundle. But Pip is asking whether the difference matters. That's a visualization question."

He pulled out a small piece of bark and a charcoal stub. He drew, very carefully, two columns side by side.

The North column went up to 65. The South column went up to 75.

The South column was taller. But it was not much taller. The two columns looked almost the same height.

He held it up so Pip could see.

"Look," he said. "When you only saw the totals as numbers, seventy-five versus sixty-five sounded like a big difference. When you see them as bars, the difference is small. The bars are almost the same height."

Pip squinted. "They're almost the same."

"They're almost the same."

"So south is barely better."

"South is barely better."

Display flipped the bark over. He drew a different graph on the back. This one was a line chart — day on the bottom, acorns on the side. He plotted a few sample days: north on Day 1 was 5, south on Day 2 was 8, north on Day 3 was 3, south on Day 4 was 6.

"Look at this one," he said. "Same data. Different picture. Now you can see whether some days were much better than others on each slope."

Pip stared at it. He could see it now. The line for the south slope had a spike on day 14 — twelve acorns in one day. The line for the north slope had a spike on day 27 — fifteen acorns in one day.

"There was one really good day on the north slope," Pip said. "Better than any day on the south."

"Yes," Display said. "And there was one really good day on the south slope, almost as good. The averages are similar. The shapes are different. Each slope has a good day hiding somewhere. The averages cover that up."