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Grade 7 · Statistics

Garden measurements: Test a summary against all readings

Garden measurements investigation: test a summary against all readings. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.

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

Watch the relationship

Paused
Garden measurements: Test a summary against all readings. Readings shown: 1 of 5. Full-data mean: 10.6. Full-data median: 11. Full-data range: 15Five readings; three different summaries[3, 5, 11, 16, 18]06121824Full-data mean 10.6 · median 11Repeated readings count separately.
This is a constructed five-observation data set, not a random sample or a measured survey. Repeated values count separately. The axis uses a fixed 0-to-24 measurement scale; all chosen readings are within it.

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.

Readings shown
1 of 5
Full-data mean
10.6
Full-data median
11
Full-data range
15

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.

A data set can have several different useful summaries. The mean balances all five values, the median is the middle after sorting, and the range is the largest minus the smallest. These numbers describe the particular data shown; they do not establish a population fact. This investigation begins with first pair anchor a = 3; single reading b = 11; second pair anchor c = 16. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.

A relationship to keep

mean = sum/5; median = sorted middle; range = max−min

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

  1. STEP 1

    Represent the given quantities

    The five readings are a, a+2, b, c, and c+2. Read each once even when two values coincide.

  2. STEP 2

    Follow the changing model

    Playback reveals the observations one at a time; the summary readouts always describe the complete five-reading set.

  3. STEP 3

    Check and explain the relationship

    Sort the full data for the median, and compare its response with the mean when changing one reading.

Your turn to explain

Make a prediction. Test your reasoning.

Garden measurements: Find the mean, median, and range of [3, 5, 11, 16, 18].

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

Compare your explanation

Mean 10.6, median 11, range 15. Sort before selecting the median.

Work through a full lesson

Connect the animation to a worked example and practice questions.

Grade 7 · Statistics

Measure spread with mean absolute deviation

Mean absolute deviation averages distances from the mean, describing variability in the original units.