Standard Deviation Visualization

About This MicroSim

This MicroSim demonstrates the concept of standard deviation — a measure of how spread out a set of experimental readings are around the mean. The histogram shows 300 randomly generated data points binned into equal intervals along the "Experimental Value" axis. The shaded blue band marks the ±1 SD zone (containing approximately 68% of all readings), and the double-headed arrow on the chart shows the exact width of 1 standard deviation.

How to Use

Slider — drag left toward "Low Standard Deviation" to make the data cluster tightly around the mean, or drag right toward "High Standard Deviation" to spread it out. The "1 SD = X.X" arrow updates immediately.
Regenerate Data button — click to draw a new random sample at the current SD setting. Use this to see how the same SD produces different-looking histograms each time (sampling variability).
Hover over any bar to see the exact value range and count for that bin.

Key Concepts

Term	Meaning
Mean (μ)	The center of the distribution (fixed at 50 in this sim)
Standard deviation (σ)	Average distance of each data point from the mean
±1 SD zone	The shaded region; contains ~68% of all data points
Bin	A 5-unit interval on the x-axis; bar height = count of readings in that interval

Iframe Embed Code

<iframe src="https://dmccreary.github.io/biology/sims/standard-deviation/main.html"
        height="500"
        width="100%"
        scrolling="no"></iframe>

Lesson Plan

Grade Level

9–12 (AP Biology, AP Statistics, or introductory data analysis)

Duration

10–15 minutes

Prerequisites

Basic understanding of mean and average
Familiarity with bar graphs and histograms

Activities

Predict (2 min): Before moving the slider, ask students — "If every experimental reading gave exactly the same result, what would the histogram look like?"
Explore low SD (3 min): Move the slider to the far left. Observe the tall, narrow peak. Click Regenerate Data several times — does the shape change much?
Explore high SD (3 min): Move the slider to the far right. Notice how the bars flatten and widen. Where does the shaded ±1 SD band extend now?
Connect to biology (5 min): Discuss examples of low-SD vs. high-SD data in biology experiments — e.g., a precise pipette measurement (low SD) vs. individual organism body masses in a population (higher SD).

Assessment

Describe in one sentence what a large standard deviation tells you about an experiment's data.
If the histogram is very wide and flat, is the standard deviation large or small?
Why does clicking "Regenerate Data" with the same SD produce a slightly different histogram each time?