.quartile-calculator-container {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
max-width: 700px;
margin: 20px auto;
padding: 25px;
border: 1px solid #e0e0e0;
border-radius: 10px;
background-color: #fdfdfd;
box-shadow: 0 4px 12px rgba(0, 0, 0, 0.05);
}
.quartile-calculator-container h2 {
color: #333;
text-align: center;
margin-bottom: 20px;
font-size: 26px;
}
.quartile-calculator-container .input-group {
margin-bottom: 18px;
}
.quartile-calculator-container label {
display: block;
margin-bottom: 8px;
color: #555;
font-weight: bold;
font-size: 15px;
}
.quartile-calculator-container input[type="text"] {
width: calc(100% – 22px);
padding: 12px;
border: 1px solid #ccc;
border-radius: 6px;
font-size: 16px;
box-sizing: border-box;
transition: border-color 0.3s;
}
.quartile-calculator-container input[type="text"]:focus {
border-color: #007bff;
outline: none;
}
.quartile-calculator-container button {
display: block;
width: 100%;
padding: 12px 20px;
background-color: #007bff;
color: white;
border: none;
border-radius: 6px;
font-size: 18px;
font-weight: bold;
cursor: pointer;
transition: background-color 0.3s ease;
margin-top: 20px;
}
.quartile-calculator-container button:hover {
background-color: #0056b3;
}
.quartile-calculator-container .result-display {
margin-top: 25px;
padding: 15px;
border: 1px solid #d4edda;
background-color: #e9f7ef;
border-radius: 8px;
min-height: 60px;
color: #155724;
font-size: 17px;
line-height: 1.6;
}
.quartile-calculator-container .result-display h3 {
color: #0f5132;
margin-top: 0;
margin-bottom: 10px;
font-size: 20px;
}
.quartile-calculator-container .result-display p {
margin-bottom: 8px;
}
.quartile-calculator-container .result-display strong {
color: #0f5132;
}
.quartile-calculator-container .error-message {
color: #dc3545;
font-weight: bold;
margin-top: 10px;
}
.quartile-calculator-container .calculator-article {
margin-top: 30px;
padding-top: 25px;
border-top: 1px solid #eee;
color: #333;
line-height: 1.7;
}
.quartile-calculator-container .calculator-article h3 {
color: #333;
font-size: 22px;
margin-bottom: 15px;
}
.quartile-calculator-container .calculator-article p {
margin-bottom: 15px;
}
.quartile-calculator-container .calculator-article ul {
list-style-type: disc;
margin-left: 20px;
margin-bottom: 15px;
}
.quartile-calculator-container .calculator-article li {
margin-bottom: 8px;
}
function calculateQuartiles() {
var dataInput = document.getElementById("dataPoints").value;
var dataArray = dataInput.split(',').map(Number).filter(function(n) { return !isNaN(n); });
if (dataArray.length < 4) {
document.getElementById("resultDisplay").innerHTML = "Please enter at least 4 valid numbers separated by commas to calculate quartiles.";
return;
}
dataArray.sort(function(a, b) { return a – b; });
// Helper function to calculate median
function getMedian(arr) {
var mid = Math.floor(arr.length / 2);
if (arr.length % 2 === 0) {
return (arr[mid – 1] + arr[mid]) / 2;
} else {
return arr[mid];
}
}
var n = dataArray.length;
var q2 = getMedian(dataArray); // This is the overall median
var lowerHalf = [];
var upperHalf = [];
if (n % 2 === 0) { // Even number of data points
lowerHalf = dataArray.slice(0, n / 2);
upperHalf = dataArray.slice(n / 2, n);
} else { // Odd number of data points (inclusive method: include median in both halves)
var medianIndex = Math.floor(n / 2);
lowerHalf = dataArray.slice(0, medianIndex + 1);
upperHalf = dataArray.slice(medianIndex, n);
}
var q1 = getMedian(lowerHalf);
var q3 = getMedian(upperHalf);
var iqr = q3 – q1;
var resultHTML = "Quartile Calculator
Understanding Quartiles
Quartiles are statistical measures that divide a dataset into four equal parts, each containing 25% of the data points. They are crucial for understanding the distribution, spread, and central tendency of a dataset, especially when dealing with skewed data or outliers.
What are the Quartiles?
- First Quartile (Q1): Also known as the lower quartile, Q1 represents the 25th percentile of the data. This means 25% of the data points fall below Q1, and 75% fall above it. It is essentially the median of the lower half of the dataset.
- Second Quartile (Q2): This is the median of the entire dataset, representing the 50th percentile. 50% of the data points fall below Q2, and 50% fall above it.
- Third Quartile (Q3): Also known as the upper quartile, Q3 represents the 75th percentile. This means 75% of the data points fall below Q3, and 25% fall above it. It is the median of the upper half of the dataset.
Why are Quartiles Important?
Quartiles provide a robust summary of data distribution, often used in conjunction with the median. They are less sensitive to extreme values (outliers) compared to the mean and standard deviation. Key applications include:
- Identifying Spread: The Interquartile Range (IQR), calculated as Q3 – Q1, measures the spread of the middle 50% of the data, giving an idea of data variability.
- Detecting Outliers: Data points falling significantly below Q1 or above Q3 (e.g., beyond 1.5 * IQR) are often considered potential outliers.
- Comparing Distributions: Quartiles allow for easy comparison of the spread and central tendency between different datasets.
- Box Plots: Quartiles are the fundamental components of box-and-whisker plots, a graphical representation of data distribution.
How to Calculate Quartiles Manually (Inclusive Method)
The calculator above uses a common method for calculating quartiles, often referred to as the "inclusive method" or Tukey's hinges method. Here's how it works:
- Sort the Data: Arrange all data points in ascending order from smallest to largest.
- Find the Median (Q2):
- If the number of data points (N) is odd, the median is the middle value.
- If N is even, the median is the average of the two middle values.
- Find the First Quartile (Q1):
- Consider the lower half of the dataset. If N is odd, include the overall median (Q2) in the lower half. If N is even, the lower half is simply the first N/2 data points.
- Q1 is the median of this lower half.
- Find the Third Quartile (Q3):
- Consider the upper half of the dataset. If N is odd, include the overall median (Q2) in the upper half. If N is even, the upper half is simply the last N/2 data points.
- Q3 is the median of this upper half.
- Calculate Interquartile Range (IQR): IQR = Q3 – Q1.
Example Calculation:
Let's use the dataset: [7, 1, 5, 9, 3, 11, 2]
- Sort the Data:
[1, 2, 3, 5, 7, 9, 11](N=7) - Find Q2 (Median): Since N=7 (odd), the median is the middle value, which is
5. So, Q2 = 5. - Find Q1: The lower half (including the median) is
[1, 2, 3, 5]. The median of this lower half is(2 + 3) / 2 = 2.5. So, Q1 = 2.5. - Find Q3: The upper half (including the median) is
[5, 7, 9, 11]. The median of this upper half is(7 + 9) / 2 = 8. So, Q3 = 8. - Calculate IQR: IQR = Q3 – Q1 = 8 – 2.5 = 5.5.
Using the calculator above with 1, 2, 3, 5, 7, 9, 11 will yield these results.