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The Magic 'N' is 385

If you’ve ever tried to conduct a survey or a research study without knowing exactly how large your target population is, you may have wondered: How many people do I actually need to sample to get reliable results? 


This is one of the most common questions our clients ask. Below, we’ll explore why sample size matters, share a simple formula for determining your sample size when the total population is unknown, and give you a handy “rule of thumb” number to remember.


Why Does Sample Size Matter?


Imagine you’re trying to measure customer satisfaction, test a new product concept, or gauge public opinion. If you speak to too few people, you run the risk of basing big decisions on incomplete or biased data. But if you try to interview everyone, you might spend all your time and money on data collection—especially if you don’t even know how large your audience really is.


A properly chosen sample size helps you:


  1. Save time and resources—You talk to enough people to get good data, but not so many that you blow your budget.


  2. Increase accuracy and reliability—A well-planned sample ensures your results reflect your actual audience.


  3. Make informed decisions—Confidently back up your findings with solid statistics.


The Challenge of an Unknown Population


In some cases, you have a sense of your population. For instance, you might know how many registered customers you have in a loyalty program or the number of potential voters in a district. But what if you’re researching a topic with no clear boundaries (e.g., “people who exercise outdoors”)?


In this scenario, we often assume the population is effectively infinite and use a standard sample size formula that does not require you to know the exact population size.


The Go-To Formula

The formula most researchers use for determining the sample size when the population is very large (or unknown) looks like this:



where:

  • n: Required sample size

  • z: Z-score linked to your chosen confidence level (e.g., 1.96 for 95% confidence)

  • p: Estimated proportion of people who have the characteristic or opinion you’re studying (if unknown, use 0.5)

  • e: Desired margin of error or precision (e.g., 0.05 for ±5% margin)


Why 0.5 for p? In most scenarios where you have no prior information. This is the “worst-case scenario” because it yields the largest sample size you would need. If you later discover p is actually lower or higher, your required sample size might be smaller—but using 0.5 ensures you err on the side of caution and don’t under-sample.


A Handy Example


Let’s say you want to be 95% confident in your results, with a ±5% margin of error, and you have no idea about the true proportion you’re measuring:


  1. Confidence Level (95%): z=1.96

  2. Proportion (p): 0.5

  3. Margin of Error (e): 0.05


Plugging into the formula:

Because you can’t interview a fraction of a person, round up to 385. This means, if you have absolutely no idea about your total population size, aiming for at least 385 completed responses is a solid guideline for a 95% confidence level with a ±5% margin of error.


When to Adjust This Number


  1. Different Confidence Levels: If you want a 90% or 99% confidence level, you’ll pick a different z-value. For example, 99% confidence might require a z of around 2.576, and that will increase your sample size.


  2. Smaller Margin of Error: If you want more precision—say ±3% instead of ±5%—that will also bump up the required n.


  3. Constraints & Realities: In real-world projects, budget, timeframe, and response rates may affect how many people you can survey. You might need to strike a balance between ideal sample size and practical limitations.


Applying This in the Real World


  • Online Surveys: If you’re targeting a broad audience (e.g., website visitors, online community members), treat them as infinite if you’re not sure how many will see your survey invite.


  • Street Interviews: Conducting in-person interviews at a shopping mall or event and don’t know total foot traffic? Aim for around 385 interviews for a robust sample.


  • Focus Groups or Qualitative Studies: Sample size formulas often don’t apply directly here because qualitative research serves a different purpose (depth of insight, not statistical generalization). Still, it’s helpful to understand if you’re moving on to a quantitative phase.


For many studies aiming for 95% confidence and ±5% margin of error, 385 is the “magic” number to remember

© Digital Boomerang

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