Grade 6 · Compare data summaries · 651 of 750
Compare data summaries · practice 66
Find the mean, median, and range of the five values [3, 5, 11, 14, 16]. Follow the calculation, then test the quantities in the animated example.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
Find the mean, median, and range of the five values [3, 5, 11, 14, 16].
Use this scratch space or work on paper. Your notes stay on this page and clear when you leave. Answers are for self-checking; they are not automatically graded.
A starting point
Repeated values count separately; find the middle only after sorting.
Work through the reasoning
Step 1
Translate the givens
The total is 3 + 5 + 11 + 14 + 16 = 49. With five observations, mean = 49/5 = 9.8.
Step 2
Calculate with the model
The sorted list is [3, 5, 11, 14, 16]. Its third entry, 11, is the median.
Step 3
Check and interpret
Range = largest − smallest = 16 − 3 = 13. These summaries describe this list, not a population.
The answer
Mean = 9.8; median = 11; range = 13.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
Use Play, Pause, and the timeline to inspect the construction. Reset restores the question’s original settings. The displayed assumptions describe where this model applies.
Watch the relationship
PausedHD animation studio
From experiment to screen.
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The mathematical idea
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. Starting quantities: First pair anchor a = 3; Single reading b = 11; Second pair anchor c = 14.
mean = sum/5; median = sorted middle; range = max−min
03 · Reflect and transfer
Explain what changes and why.
Which summary would be most sensitive to replacing the largest observation with a much larger one?
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.