# If I take n-standard deviations of my data what would be my confidence level with the estimate?

I have some measurement data of estimates vs actuals (of some metric $m$). For every such data I also have the ratio of $\frac{actuals}{estimates} = r \space (say)$ - if this ratio is greater than 1 it implies underestimation (and overestimation if less than one).

Given I have substantial data, about 100 or so data points, I calculate the mean $\mu$ and standard deviation $\sigma$, ($\forall \space r_i| i=1,...,100$ from above).

Based on the data above I can say that historically derived confidence range of my estimate is $\mu \pm n\sigma$ - where 'n' is the number of standard deviations I wish to consider.

Question - what can I say about my confidence level for the 'next estimate' for $n=1,...,6$?

Example:

Let's say $\mu = 1.16$ and $\sigma = 0.38$ (data points are {$r_i|i = 1,...,100$}).

For $n = 1$ the upper limit $u = 1.53$ and lower limit $v = 0.78$ (i.e., $\mu \pm n\sigma$)

Now, say I make an estimate of 100 for $m$ and using the historical data with one-standard deviation as above I can say the following about a most likely estimate:

• The estimate should be revised to $116$ (i.e., $100 \mu$) due to underestimation on 'average'
• The value is quite likely to be within $78$ and $153$ ($100u$ and $100v$)

So for $1\sigma$ (i.e., $n=1$) what is confidence level of the estimate? Is it simply just a ratio of $\frac{numbers Within Range}{Total No. of Elements}$?

If I now make $n=2$ what can I say about the confidence level of the estimate for $m$?

Basically if I have historically derived confidence ranges ($u, v$ and mean $\mu$) can I peg some sort of a percentage probability (or confidence level) of the likelihood value for the estimate of $m$? How would I do it? Should I restrict the max value of $n$ to 6? (why so?)

PS: For those in the know, this is the cone of uncertainty data calculation for a particular metric. And I'd like to know the confidence value that I can associate with my estimate as per historic data.

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