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Ratios and Data 6-8 / Week 11 / Wednesday
3/6
Week 11 · Center and Spread

Wednesday

Numbers Lab: paper ball toss
// One number for the middle, one number for the scatter
⏱ about 20 min

Wednesday: Numbers Lab, Paper Ball Toss

Rocket crumples a sheet of paper into a ball. "Field Day needs a toss game. How far can a paper ball fly?"

"That depends on the toss," Raven says. "A statistical question. We need lots of throws."

Nova marks a start line with tape. "Eight tosses each. Measure where it first lands."

Rocket throws. The ball flutters and drops. "One hundred twenty centimeters. Weak."

He throws again. "One hundred thirty-five! Better." He keeps going until eight numbers fill the sheet.

"What do you notice?" Raven asks, reading his log. "Your tosses jump around a lot."

"So my mean tells the typical toss," Rocket says. "And the MAD tells how jumpy I am."

"Now you are describing data with two numbers," Nova says. "Center and spread."

Your investigation

Today you collect eight distances and describe them with a center and a spread. The question is statistical: how far does your paper ball toss go?

You will find the mean, the median and the range, and you may try the MAD too.

  • One sheet of scrap paper, crumpled into a ball.
  • Masking tape for a start line.
  • A tape measure or a meter stick.
  • Your Numbers Notebook and a pencil.
Safety first
Toss indoors in a cleared space or outdoors on flat ground, away from roads. A grown-up picks the spot.
Toss away from people, pets, lamps and anything that could break. A soft paper ball only.
Pick up the ball and any tape after each toss so no one trips or slips.
  1. Tape a start line on the floor. Stand behind it with your toes on the tape.
  2. Toss the paper ball underhand. Measure from the line to where it first touches down, in centimeters.
  3. Write the distance in your notebook. Repeat until you have eight tosses.
  4. Put the eight distances in order. Find the median and the range.
  5. Add the eight distances and divide by 8 to find the mean.
  6. Optional: find each toss's distance from the mean and average them for the MAD.

Rocket's eight tosses

Here is Rocket's log, in the order he threw: 120, 135, 150, 128, 142, 160, 135, 130 centimeters.

In order: 120, 128, 130, 135, 135, 142, 150, 160. The least is 120 and the greatest is 160, so the range is 40.

The two middle values are 135 and 135, so the median is 135.

The eight tosses add to 1100. Divide by 8 and the mean is 137.5 centimeters.

TossDistance (cm)
1120
2135
3150
4128
5142
6160
7135
8130
ROCKET'S TOSSES
  • Read the question.
  • Tap your answer.
What is the mean of Rocket's eight toss distances, in centimeters?
What is the median of Rocket's eight toss distances?
What is the range of Rocket's eight toss distances?
How many of Rocket's tosses went farther than his mean of 137.5 centimeters? Type the number.
WHY THIS EXERCISEThe mean does not have to split the data in half. The median does. Comparing them tells you about the shape.
StatementTrue or false?
Rocket's longest toss was 160 centimeters.?
The median of eight values is the mean of the fourth and fifth values in order.?
Rocket's mean toss was longer than his median toss.?
The range uses every value in the data set.?
WHY THIS EXERCISEChecking the mean against the median is a quick test of how balanced a data set is.

Mean or median for a toss?

Rocket's mean (137.5) sits a little above his median (135). His longest toss, 160, pulled the mean up.

For a toss game, the median is a fair "typical toss". The mean is useful too, but one wild throw can tug it.

Report both when you can, and say which one you trust more for your data. That is what a careful data report does.

Try it
Toss eight more times with your other hand. Find the median of the new set.
Which hand has the higher median? Which hand has the wider range?
For a grown-up
Today's lab is an underhand paper ball toss with a tape measure. Please choose a clear, flat spot away from breakables.
If a tape measure is not handy, floor tiles or a length of string marked in hand spans work as units.

Center and spread from your own throws. Tomorrow the crew compares two groups of kids on the sack hop course.

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