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A Sample of 3,000

To experience firsthand a simulation of randomly sampling 3,000 participants from a population. Imagine that for the US population, people spent on average 15 hours a week on social media. What's more, 68% of the population spent 12 to 18 hours a week on social media. How well could a sample of 3,000 participants represent the entire population?

Directions

Below is the Begin button, a histogram of the population (in terms of their Social Media Usage), and a histogram of the sample. Once you click begin, participants (represented by a yellow dot) will be randomly selected one at a time from the population. After each participant is selected, the bottom histogram will be updated. The simulation stops when all 3,000 participants have been randomly selected. At that point, compare the sample mean with the population mean. As a representative sample, we would expect the sample and population mean to be very similar. Any difference between them would be considered an error, and referred to as sampling error. You may restart the simulation by clicking the "Begin" button.

Controls

Starts a fresh run, clearing previous dots and the sample histogram. Keyboard: Space also begins.

Population

Population distribution: mean = 15 hours/week, standard deviation = 3. X-axis ticks every 3 from 0 to 27. Y-axis is proportion up to 0.25 with ticks every 0.05.

Population distribution of social media hours A smooth green normal curve with mean at 15 hours. Yellow dots appear along the baseline for each sampled participant. A blue dashed vertical cursor marks the most recently sampled value. A black vertical line marks the population mean.
Population mean: 15.000 hours/week

Sample

Sample histogram updates after each draw (bin size = 1 hour). Y-axis is proportion and rescales to 0.05 above the tallest bin (rounded up to the next 0.05), starting at 1.00 for the first draw. X-axis ticks every 3 from 0 to 27. Bars are blue with thin black borders; a black vertical line marks the sample mean.

Sample histogram of social media hours Blue bars show the distribution of sampled participants, as a proportion. The vertical scale adapts as more data arrive. A black line shows the current sample mean.
Sample size: 0
Sample mean: —
Current y-axis max (proportion): 1.00

Sample Mean Updates

Rows appear after every draw up to n = 10, then every 10 draws up to n = 100, and every 100 draws thereafter.
Rows show the cumulative sample size and sample mean at the following increments: every draw up to n = 10, every 10 draws up to n = 100, and every 100 draws thereafter.
Sample size Sample mean