# Determine whether a number “fits” with a group of numbers

I need to determine if a single number "fits" with a group of numbers. All the numbers will be percentages, so we'll use decimals.

For example:

The group is: 0.1, 0.25, 0.3, 0.4, 0.9 and we'll test against two single numbers: $y_1$ = 0.2 and $y_2$ = 0.8

The group is all low numbers, except for the one outlier, 0.9.

So I need to know that $y_1$ fits in with the group, but $y_2$ doesn't.

I'm thinking I need to do confidence interval. So I take the median of the group, in this case 0.3, then check to see if the single number is within a tolerance of the median. So in this example, if the single number is "good" it should be within the range 0.3 +/- 0.2. But how do you find that tolerance?

Note: this is not a math homework problem, so I don't get mean or variance or anything just handed to me. All I have to work with are the group of numbers and the single number.

• May I ask what the purpose of the outlier detection is here? Is determining that $.9$ doesn't fit of scientific interest here, or are you looking for a way of weeding out "bad" observations, such as measurement errors? – Macro May 8 '12 at 3:26