Compare Means and Variation
Use a range and overlapping results alongside group means.
Supplied materials
- Use the supplied fictional observations or model. Paper and pencil are optional; spoken answers are welcome. No equipment or real experiment is needed.
Learn the idea
A mean summarizes a group but hides the individual values. Also inspect the range: the minimum through the maximum. If two groups share values, it would be wrong to say every individual in one exceeds every individual in the other. Neither overlap nor a mean difference alone decides whether a larger study would support an effect.
New fictional light-test growths are L: 2, 4, 6 cm and S: 1, 3, 5 cm. Same species, starting size, pots, water, temperature, and one-week duration are specified. L averages 4 cm and S averages 3 cm. Their ranges overlap from 2 through 5 cm. Describe the observed difference and the variation without using this small data set as a universal plant rule.
- Compute both means from the three values.
- Find each minimum and maximum.
- Compare L’s 2 cm with S’s 5 cm to test an all-individuals claim.
- Write a sentence including the 1 cm mean difference and overlapping ranges.
See the method in action
L mean = (2 + 4 + 6)/3 = 4 cm; range 2–6. S mean = (1 + 3 + 5)/3 = 3 cm; range 1–5. L’s mean is 1 cm higher, but its smallest result is below S’s largest.
Check your reasoning
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See the answer and explanation
L’s mean is 1 cm higher, and the ranges overlap.
The means are 4 and 3. Both groups vary, and values from their minimum–maximum spans overlap.
Take it further
Change L to 4, 4, 4 cm. Its mean stays 4 cm, but its range is now 4–4; the same mean can describe a different amount of variation.
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Check the subject sources
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