The Tolerance Interval Calculator is a tool used to estimate the population mean and standard deviation given a sample size and confidence level. It is useful for finding the range of values within which a given proportion of the population lies. This calculator can help to identify how much uncertainty exists in a given set of data.
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A tolerance interval is a range that is likely to contain a specific proportion of a population with a certain level of confidence.
This calculator creates a tolerance interval based on a given sample.
Simply enter a list of sample values below, then choose a proportion of the population you’d like the tolerance interval to contain, then choose a confidence level, then click the “Calculate” button:
Sample values:
Proportion of Population:
Confidence Level:
95% Tolerance Interval: (15.102, 73.565)
function calc() {
//get input data
var x = document.getElementById(‘x’).value.split(‘,’).map(Number);
var pop = +document.getElementById(‘pop’).value;
var CI = +document.getElementById(‘CI’).value;
var CI_out = CI*100
var xbar = math.mean(x);
var n = x.length;
var s = math.std(x);
var z = Math.abs(jStat.normal.inv((1-pop)/2, 0, 1));
var blob = Math.sqrt(((n-1)*(1+1/n))/(jStat.chisquare.inv(1-CI, n-1)));
console.log(xbar, n, s, z, blob);
//calculate lower and upper bounds of prediction interval
var lowCI = xbar-s*z*blob;
var highCI = xbar-(-1*s*z*blob);
//output results
document.getElementById(‘lowCI’).innerHTML = lowCI.toFixed(3);
document.getElementById(‘highCI’).innerHTML = highCI.toFixed(3);
document.getElementById(‘CI_out’).innerHTML = CI_out.toFixed(0);
} //end calc function