Montana Math MT.PLUS.DATA.DES.3.a
The Standard
- MT.PLUS.DATA.DES.3
- Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic by: Simulating a sampling distribution of sample means from a population with a known distribution, observing the effect of the sample size on the variability, and Demonstrating that the standard deviation of each simulated sampling distribution is the known standard deviation of the population divided by the square root of the sample size.
Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic by: Simulating a sampling distribution of sample means from a population with a known distribution, observing the effect of the sample size on the variability, and
2026 Montana Mathematics Content Standards · Data Reasoning
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students repeatedly draw random samples with replacement from a population with known values. They calculate one mean per sample, then compare how spread out the means are for small and large samples.
What Mastery Looks Like
- Students plot sample means for two sample sizes and identify which set has less spread. They explain that larger samples tend to give means closer to the population mean.
Common Misconceptions
- Students may plot every individual draw instead of one mean per sample. They may think a larger sample changes the population mean or guarantees a mean closer to it.
How to Assess It
- Exit ticket: A cup holds four 0 slips and four 10 slips. After 30 samples of size 2 and 30 of size 8, with replacement, which set of sample means should be more spread out, and where should both center?
Lesson moves
Ways to Teach It
Put four 0 slips and four 10 slips in a cup; draw with replacement, then plot 10 sample means each for sizes 2 and 8.
Ask students: Why do size-8 averages cluster around 5 when every slip shows either 0 or 10?
Give pairs unlabeled dot plots of sample means from the cup; have them label size 2 or 8 and explain their choices.
Use a printed list of 20 bus delays; sample with replacement to compare average delays from samples of 3 rides and 10 rides.
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Related Standards
- MT.PLUS.DATA.INF.2
Estimate a population parameter from a representative sample by: Understanding why the sample statistic is the best estimate for the associated population param...
- MT.PLUS.DATA.DES.3
Evaluate the effect of sample size on the expected variability in the sampling distribution of a sample statistic by: Simulating a sampling distribution of samp...
- MT.PLUS.DATA.INF.2.b
Understanding that sampling variability introduces uncertainty in the estimate, and account for the uncertainty with a confidence interval by: Using resamplin...
- MT.PLUS.DATA.DES.3.b
Demonstrating that the standard deviation of each simulated sampling distribution is the known standard deviation of the population divided by the square root o...
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