For a statistical sample with a 95% confidence level, explain what occurs that other 5% of the time. Is that sample more likely to be close (but not within) the margin or error than to be far away?

Question

For a statistical sample with a 95% confidence level, explain what occurs that other 5% of the time. Is that sample more likely to be close (but not within) the margin or error than to be far away?

In: Mathematics

Answer 1

> Is that sample more likely to be close (but not within) the margin or error than to be far away?

It depends on the distribution. But for what you’re thinking of, the answer is most likely yes. You’re probably thinking of a Gaussian curve (“bell curve”) and it [looks like this](https://miro.medium.com/max/24000/1*IdGgdrY_n_9_YfkaCh-dag.png).

In a bell curve, 95% of the data is within 2 **standard deviations** of the **average**. For example, a person’s IQ has a **standard deviation of 15** and an **average of 100**.

2 standard deviations is then 30. So within 30 of 100, really means as low as 70 or as high as 130. 95% of people will have an IQ between 70-130.

5% of people have an IQ outside of 70-130, but you’re correct to assume you’ll see most of this 5% hover around 69 or 131 instead of some outlandish IQs like 170. Let’s go back to the [picture of a bell curve](https://miro.medium.com/max/24000/1*IdGgdrY_n_9_YfkaCh-dag.png) I showed you…

* “Within 1 standard deviation” is marked by the pink color. In the IQ example, that would be the range of 85-115.
* “Within 2 standard deviations” is the pink color **and** the blue color. In the IQ example, that would be 70-130.
* “Outside of 2 standard deviations” is the other 5%. But you see how there’s more green than orange? Your guess is correct: even if you’re outside 95%, you’re still likely to be close to it (green) than you are to be far away from it (orange).