| Participant ID | Age (years) | Caffeine intake (mg) |
|---|---|---|
| 134718 | 10 | 13 |
Central Limit Theorem (CLT)
Lily Koffman
Department of Biostatistics, Johns Hopkins School of Public Health
Learning objectives
Describe how changing sample size impacts the distribution of the sample mean
Explain how the Central Limit Theorem quantifies the uncertainty of a sample mean
Question: what is the average daily caffeine consumption among Americans?
How might we answer this question?
We could survey every single American
We could take a sample
Sample one person
Add another person to sample and calculate average
| Participant ID | Age (years) | Caffeine intake (mg) | Sample mean (cumulative) |
|---|---|---|---|
| 134718 | 10 | 13 | 13 |
| 132129 | 10 | 121 | 67 |
Add more people to sample
| Participant ID | Age (years) | Caffeine intake (mg) | Sample mean (cumulative) |
|---|---|---|---|
| 134718 | 10 | 13 | 13 |
| 132129 | 10 | 121 | 67 |
| 132137 | 43 | 102 | 79 |
| 141998 | 52 | 144 | 95 |
| 133390 | 49 | 192 | 114 |
| 140734 | 6 | 4 | 96 |
| 136086 | 15 | 0 | 82 |
| 135573 | 70 | 202 | 97 |
| 135693 | 30 | 360 | 126 |
| 140558 | 59 | 0 | 114 |
Lily’s sample
Lily’s sample
What if someone else went out and sampled different people?
A different sample
