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Grade 5 · Statistics

River-study stations: redistribute data without changing the total

Three measured amounts at a river study are 6, 14, and 8 units. Change the controls and explain what the animation reveals.

Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.

Watch the relationship

Paused
River-study stations: redistribute data without changing the total. Unchanged total: 28. Mean / equal share: 9.333. First group now: 6Fixed total 28 · mean 9.3336A14B8CAmounts can move; their combined total stays fixed.
Amounts can be divided continuously, so fractional shares are allowed. The model redistributes a fixed total among exactly three groups. Decimals are rounded while fraction answers remain exact.

Starts paused. Play once, pause anywhere, or use Step to inspect the mathematics. Playback stops when this panel leaves the screen.

Make it your experiment

Change one value. Notice what follows.

The controls adjust the model. Numbers below describe the current frame. Decimals are rounded.

Unchanged total
28
Mean / equal share
9.333
First group now
6

HD animation studio

From experiment to screen.

Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.

Understand what you are seeing

The idea behind the motion.

Three measured amounts at a river study are 6, 14, and 8 units. The arithmetic mean is the common amount obtained by redistributing a fixed total equally. Each group's amount may change during sharing, but the combined total remains unchanged. The total is 28. Each equal share is exactly 28/3 units, even when the decimal representation repeats.

A relationship to keep

Mean = (6 + 14 + 8) / 3 = 9.333 approximately

Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.

  1. STEP 1

    Read the starting situation

    Three measured amounts at a river study are 6, 14, and 8 units. Identify what each number measures before changing a control; the worked example refers to these starting values.

  2. STEP 2

    Follow the mathematical change

    Move the timeline to redistribute amounts toward three equal bars. Check that no material is created or lost while the bar heights become equal. Pause on an intermediate frame and compare the picture with the live readouts.

  3. STEP 3

    Explain and test the relationship

    The total is 28. Each equal share is exactly 28/3 units, even when the decimal representation repeats. Change one input, predict its effect, and test whether the same relationship still works.

Your turn to explain

Make a prediction. Test your reasoning.

River-study stations: use the original situation. Three measured amounts at a river study are 6, 14, and 8 units. What is the exact equal share, and how can it be checked?

Use the values specified in the question. Reset restores the initial values for this investigation.

Compare your explanation

28/3 units per group. Multiplying this by 3 recovers the total 28.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 5 · Statistics

Understand the mean as a fair share

Find an arithmetic mean by redistributing a fixed total equally.