Question

Compare Jeremy’s sample to Morgan’s.

Morgan’s Sample as a data table and histogram with Jeremy’s Sample as a data table and histogram. The numbers are distributed differently in each sample. They have mostly different members, but are each likely to be representative of the population.

Answer 1

Short answer
- Both samples appear to come from the same population in the sense that neither shows obvious bias, but they are distributed differently (different shapes/centers/spreads) and have mostly different members. Those differences are expected from random sampling and do not by themselves prove one sample is unrepresentative.

How to compare them (practical checklist)
1. Put the data side-by-side
- Show both data tables and place their histograms next to each other (or overlay density curves). This makes differences in shape, center and spread obvious.

2. Compare basic summary statistics
- Center: mean and median for each sample.
- Spread: standard deviation (or IQR) and range.
- Shape: skewness and modality (uniform/uni/bi/multimodal).
- Outliers: any extreme values present in one sample but not the other.

3. Look at visual features
- Are the histograms peaked in different places? One skewed while the other is symmetric?
- Do the bins with the highest frequency differ?
- How much overlap is there between the two distributions?

4. Assess representativeness
- Check sample size and sampling method. Random samples of adequate size are usually representative even if they differ from one another.
- If sample sizes are small or sampling was nonrandom (convenience, self-selected), representativeness is weaker.
- Compare sample summaries to known population parameters (if available).

5. Formal checks (if you want statistical evidence)
- Two-sample t-test (or Welch’s t-test) to test for a difference in means.
- Mann–Whitney U test to compare medians if assumptions fail.
- Kolmogorov–Smirnov test or Anderson–Darling test to compare full distributions.
- Levene’s test for equality of variances.
- Report effect sizes (e.g., Cohen’s d) and confidence intervals, not just p-values.

Interpretation you can use in a report
- “Morgan’s sample and Jeremy’s sample contain mostly different individuals and the histograms show different distributions (Morgan: [describe shape]; Jeremy: [describe shape]).”
- “Despite those differences, both samples appear plausibly representative of the population because [they were randomly drawn / sample sizes are adequate / neither shows a sampling bias].”
- “Differences between the samples are consistent with sampling variability. To evaluate whether these differences are statistically meaningful, we performed [test] and found [result, effect size, CI].”
- If you don’t run tests: “Visual and summary-statistic comparisons suggest [which sample has higher center, which is more spread], but formal testing is needed to determine whether the differences are statistically significant.”

Recommended next steps
- Compute the summary statistics and overlay the histograms (or density plots).
- Run the appropriate statistical tests listed above.
- If representativeness is critical, increase sample sizes or use stratified sampling to reduce random differences.

If you want, paste both samples (the raw numbers) and I will:
- produce the data tables and histograms,
- compute summary statistics,
- run appropriate tests and give a short written conclusion.