Normal Distribution
Your external evaluator reads your draft outcomes report and asks, "Have you checked whether the scores are normally distributed?" You vaguely remember bell curves from a statistics class in university, but that was a long time ago. You know the shape, the symmetrical hump that's high in the middle and tails off on both sides. But you're not sure what it means for your data to "be" one of those, or why anyone would care.
The normal distribution is the bell curve's formal name. It is the single most important shape in statistics. It's a specific pattern where most values cluster around the center and become progressively rarer as you move further out in either direction. The left side mirrors the right side exactly. And it shows up often enough in the real world (human heights, blood pressure readings, standardized test scores) that statisticians built their most powerful tools around it.
A normal distribution is completely described by two numbers you already know. The mean tells you where the center of the bell sits. The standard deviation tells you how wide it spreads. A small standard deviation gives you a tall, narrow bell. A large one gives you a short, wide bell. But the shape is always symmetrical, with the mean, median, and mode all sitting at the exact same point.
The most useful property of the normal distribution is how predictable it is. About 68% of all values fall within one standard deviation of the mean. About 95% fall within two standard deviations. And about 99.7% fall within three. This is sometimes called the 68-95-99.7 rule, and it holds every time for normally distributed data. If your program's outcome scores have a mean of 50 and a standard deviation of 10, then roughly 68% of participants scored between 40 and 60. About 95% scored between 30 and 70. A score below 20 or above 80 would be extremely rare, happening less than 0.3% of the time.
This predictability is what makes the normal distribution so central to statistical analysis. Confidence intervals, hypothesis tests, and many of the tools we'll cover in future entries all rely on this shape to calculate how likely or unlikely a result is. When your data is normally distributed, those tools work as advertised. When it's not, the answers can be misleading.
But here's the tension. As we explored in the entry on skewness, most nonprofit data is not normally distributed. Donation amounts are almost always right-skewed. Event attendance often clusters in two groups rather than one smooth bell. Survey responses on a 1-to-5 scale can't follow a normal distribution because they're bounded and discrete. The normal distribution is a theoretical ideal, and real data deviates from it to varying degrees. That doesn't make it useless. Many statistical procedures are surprisingly forgiving of moderate departures from normality, especially with larger sample sizes. And some nonprofit datasets genuinely do approximate this shape. Program outcome scores on well-designed assessments, differences between pre-test and post-test results, and measurement errors all tend to be roughly normal. The key is to check rather than assume. A quick look at a frequency distribution will tell you whether the bell curve is a reasonable approximation or whether you need different tools.
In program evaluation, whether your outcome data is normally distributed determines which statistical tests are valid for your analysis, which is exactly why evaluators ask about it. In fundraising analytics, the 68-95-99.7 rule can help you set realistic benchmarks. If your monthly online revenue has a mean of €15,000 and a standard deviation of €3,000, then a month below €9,000 would be genuinely unusual and worth investigating, not a reason to panic. In grant reporting, showing that your data approximates a normal distribution, or explaining how it differs, signals statistical literacy that strengthens your credibility with funders.
The normal distribution is the shape statistics was built around. Your data doesn't need to match it perfectly, but you need to know when it's close enough and when it's not.
See It
Drag the slider to change the standard deviation. Watch how the same percentage bands (68%, 95%, 99.7%) cover a wider or narrower range of scores as the spread changes.
Reflect
Think about a metric your organization reports to funders or uses in program evaluation. Have you ever checked whether the data is roughly symmetrical, or do you assume it follows a bell curve without looking? What might you discover if you plotted every value?
When a monthly result comes in much higher or lower than expected, how does your team decide whether to worry? Could knowing the standard deviation of that metric help you tell the difference between normal variation and a genuine signal?