The Interquartile Range (IQR) is a measure of statistical dispersion, representing the range of the middle 50% of your data. It is calculated as the difference between the third quartile (Q3) and the first quartile (Q1). The IQR is less sensitive to outliers than the overall range of the data, making it a robust measure of variability.
How to Calculate the IQR:
To calculate the IQR, you first need to find the first quartile (Q1) and the third quartile (Q3) of your dataset.
Sort the Data: Arrange your data points in ascending order.
Find the Median (Q2): Determine the median of the entire dataset. This is the middle value. If there's an even number of data points, the median is the average of the two middle values.
Find the First Quartile (Q1): Q1 is the median of the lower half of the data. This is the set of data points below the overall median (Q2). If the overall median is one of the data points, it is NOT included in the lower half.
Find the Third Quartile (Q3): Q3 is the median of the upper half of the data. This is the set of data points above the overall median (Q2). If the overall median is one of the data points, it is NOT included in the upper half.
Calculate the IQR: Subtract Q1 from Q3: IQR = Q3 - Q1
Use Cases for IQR:
Identifying Outliers: The IQR is often used to detect potential outliers. Data points that fall below Q1 - 1.5 * IQR or above Q3 + 1.5 * IQR are often considered outliers.
Describing Data Spread: It provides a concise way to understand how spread out the central portion of your data is.
Comparing Datasets: The IQR can be used to compare the variability of different datasets, especially when they may have different scales or distributions.
Robustness: Its resistance to extreme values makes it more reliable than the simple range in datasets with potential outliers.
Example:
Let's calculate the IQR for the dataset: 5, 10, 12, 15, 18, 20, 25
Sorted Data: The data is already sorted: 5, 10, 12, 15, 18, 20, 25.
Median (Q2): There are 7 data points. The median is the 4th value, which is 15.
Lower Half: The data points below 15 are: 5, 10, 12. The median of this lower half (Q1) is 10.
Upper Half: The data points above 15 are: 18, 20, 25. The median of this upper half (Q3) is 20.
IQR:IQR = Q3 - Q1 = 20 - 10 = 10. The Interquartile Range is 10.
function calculateIQR() {
var dataInput = document.getElementById("dataPoints").value;
var resultDiv = document.getElementById("result");
var resultValueDiv = document.getElementById("result-value");
if (!dataInput) {
alert("Please enter data points.");
resultDiv.style.display = 'none';
return;
}
var dataArray = dataInput.split(',')
.map(function(item) { return parseFloat(item.trim()); })
.filter(function(item) { return !isNaN(item); });
if (dataArray.length === 0) {
alert("No valid numbers were entered. Please check your input.");
resultDiv.style.display = 'none';
return;
}
dataArray.sort(function(a, b) { return a – b; });
var q1, q3;
var len = dataArray.length;
var midIndex = Math.floor(len / 2);
if (len % 2 === 1) {
// Odd number of data points
var lowerHalf = dataArray.slice(0, midIndex);
var upperHalf = dataArray.slice(midIndex + 1);
q1 = calculateMedian(lowerHalf);
q3 = calculateMedian(upperHalf);
} else {
// Even number of data points
var lowerHalf = dataArray.slice(0, midIndex);
var upperHalf = dataArray.slice(midIndex);
q1 = calculateMedian(lowerHalf);
q3 = calculateMedian(upperHalf);
}
var iqr = q3 – q1;
resultValueDiv.innerText = iqr;
resultDiv.style.display = 'block';
}
function calculateMedian(arr) {
var len = arr.length;
if (len === 0) return 0; // Should not happen with valid inputs
var mid = Math.floor(len / 2);
if (len % 2 === 1) {
return arr[mid];
} else {
return (arr[mid – 1] + arr[mid]) / 2;
}
}