body {
font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
background-color: #f8f9fa;
color: #333;
margin: 0;
padding: 20px;
display: flex;
flex-direction: column;
align-items: center;
}
.loan-calc-container {
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
width: 100%;
max-width: 700px;
margin-bottom: 30px;
}
h1, h2 {
color: #004a99;
text-align: center;
margin-bottom: 20px;
}
.input-group {
margin-bottom: 15px;
display: flex;
flex-direction: column;
}
.input-group label {
margin-bottom: 8px;
font-weight: 600;
color: #004a99;
}
.input-group input[type="text"],
.input-group input[type="number"] {
padding: 10px;
border: 1px solid #ced4da;
border-radius: 4px;
font-size: 1rem;
width: calc(100% – 22px); /* Adjust for padding and border */
}
.input-group input[type="text"]:focus,
.input-group input[type="number"]:focus {
border-color: #004a99;
outline: none;
box-shadow: 0 0 0 0.2rem rgba(0, 74, 153, 0.25);
}
button {
background-color: #004a99;
color: white;
padding: 12px 20px;
border: none;
border-radius: 4px;
font-size: 1.1rem;
cursor: pointer;
transition: background-color 0.3s ease;
width: 100%;
margin-top: 10px;
}
button:hover {
background-color: #003366;
}
#result {
margin-top: 25px;
padding: 20px;
border: 1px dashed #004a99;
border-radius: 8px;
background-color: #e7f3ff;
text-align: center;
font-size: 1.4rem;
font-weight: bold;
color: #003366;
}
#result p {
margin: 5px 0;
}
#result span {
color: #28a745;
}
.article-content {
width: 100%;
max-width: 700px;
background-color: #ffffff;
padding: 30px;
border-radius: 8px;
box-shadow: 0 4px 15px rgba(0, 0, 0, 0.1);
line-height: 1.7;
text-align: left;
}
.article-content h2 {
text-align: left;
margin-top: 0;
}
.article-content p {
margin-bottom: 15px;
}
.article-content code {
background-color: #e9ecef;
padding: 2px 5px;
border-radius: 3px;
font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
}
.formula {
background-color: #e9ecef;
padding: 10px;
border-radius: 5px;
margin: 10px 0;
overflow-x: auto;
}
@media (max-width: 600px) {
.loan-calc-container, .article-content {
padding: 20px;
}
button {
font-size: 1rem;
}
#result {
font-size: 1.2rem;
}
}
Understanding Statistical Measures
Statistics is the science of collecting, analyzing, interpreting, presenting, and organizing data. Understanding key statistical measures allows us to make sense of data sets, identify trends, and draw meaningful conclusions. This calculator provides insights into several fundamental statistical measures.
Mean (Average)
The mean is the sum of all values in a data set divided by the number of values. It's a common measure of central tendency, representing the "average" value.
Mean = (Sum of all data points) / (Number of data points)
For example, if your data points are 10, 15, 22, 8, 12:
Sum = 10 + 15 + 22 + 8 + 12 = 67
Number of data points = 5
Mean = 67 / 5 = 13.4
Median
The median is the middle value in a data set that has been ordered from least to greatest. If there is an even number of data points, the median is the average of the two middle values. The median is less affected by extreme outliers than the mean.
To find the median:
- Sort the data points in ascending order.
- If there's an odd number of points, the median is the middle value.
- If there's an even number of points, the median is the average of the two middle values.
Using our example data (10, 15, 22, 8, 12), sorted: 8, 10, 12, 15, 22. The middle value is 12. So, the Median = 12.
If the data was 8, 10, 12, 15, 22, 25: The two middle values are 12 and 15. Median = (12 + 15) / 2 = 13.5.
Mode
The mode is the value that appears most frequently in a data set. A data set can have one mode (unimodal), more than one mode (multimodal), or no mode if all values appear with the same frequency.
In the data set 10, 15, 22, 8, 12, 15, each number appears once, except for 15 which appears twice. So, the Mode = 15.
In the data set 5, 5, 7, 7, 9, both 5 and 7 are modes.
In the data set 1, 2, 3, 4, 5, there is no mode.
Range
The range is the difference between the highest and lowest values in a data set. It gives a simple indication of the spread of the data.
Range = Maximum Value – Minimum Value
For the data set 10, 15, 22, 8, 12:
Maximum Value = 22
Minimum Value = 8
Range = 22 – 8 = 14
Standard Deviation
Standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
The formula for the sample standard deviation (commonly used when analyzing a subset of a larger population) is:
Standard Deviation (s) = √ Σ(xᵢ – &bar;x)² / (n – 1)
Where:
s is the sample standard deviationΣ denotes summationxᵢ represents each individual data point&bar;x is the mean of the data setn is the number of data points
Steps:
- Calculate the mean (&bar;x).
- For each data point (xᵢ), subtract the mean and square the result: (xᵢ – &bar;x)².
- Sum up all the squared differences from step 2.
- Divide the sum by (n – 1), where n is the number of data points. This gives the variance.
- Take the square root of the variance to get the standard deviation.
For data set 10, 15, 22, 8, 12 (n=5, mean=13.4):
- (10 – 13.4)² = (-3.4)² = 11.56
- (15 – 13.4)² = (1.6)² = 2.56
- (22 – 13.4)² = (8.6)² = 73.96
- (8 – 13.4)² = (-5.4)² = 29.16
- (12 – 13.4)² = (-1.4)² = 1.96
- Sum of squared differences = 11.56 + 2.56 + 73.96 + 29.16 + 1.96 = 119.2
- Variance = 119.2 / (5 – 1) = 119.2 / 4 = 29.8
- Standard Deviation = √29.8 ≈ 5.46
Use Cases
These statistical measures are vital across many fields:
- Education: Analyzing student test scores.
- Finance: Assessing investment risk and performance.
- Science: Interpreting experimental results.
- Healthcare: Tracking patient outcomes and disease prevalence.
- Market Research: Understanding consumer behavior and preferences.
function calculateStatistics() {
var dataInput = document.getElementById("dataInput").value;
var resultElement = document.getElementById("result");
var meanResultElement = document.getElementById("meanResult");
var medianResultElement = document.getElementById("medianResult");
var modeResultElement = document.getElementById("modeResult");
var rangeResultElement = document.getElementById("rangeResult");
var stdDevResultElement = document.getElementById("stdDevResult");
// Clear previous results
meanResultElement.textContent = "-";
medianResultElement.textContent = "-";
modeResultElement.textContent = "-";
rangeResultElement.textContent = "-";
stdDevResultElement.textContent = "-";
var dataPoints = dataInput.split(',')
.map(function(item) {
return parseFloat(item.trim());
})
.filter(function(item) {
return !isNaN(item);
});
if (dataPoints.length === 0) {
alert("Please enter valid numerical data points separated by commas.");
return;
}
// — Calculations —
// Mean
var sum = dataPoints.reduce(function(acc, val) {
return acc + val;
}, 0);
var mean = sum / dataPoints.length;
meanResultElement.textContent = mean.toFixed(4);
// Median
var sortedData = dataPoints.slice().sort(function(a, b) {
return a – b;
});
var median;
var mid = Math.floor(sortedData.length / 2);
if (sortedData.length % 2 === 0) {
median = (sortedData[mid – 1] + sortedData[mid]) / 2;
} else {
median = sortedData[mid];
}
medianResultElement.textContent = median.toFixed(4);
// Mode
var freqCounter = {};
var maxFreq = 0;
var modes = [];
dataPoints.forEach(function(item) {
freqCounter[item] = (freqCounter[item] || 0) + 1;
if (freqCounter[item] > maxFreq) {
maxFreq = freqCounter[item];
}
});
if (maxFreq > 1) {
for (var item in freqCounter) {
if (freqCounter[item] === maxFreq) {
modes.push(parseFloat(item));
}
}
modeResultElement.textContent = modes.join(', ');
} else {
modeResultElement.textContent = "No mode";
}
// Range
var min = sortedData[0];
var max = sortedData[sortedData.length – 1];
var range = max – min;
rangeResultElement.textContent = range.toFixed(4);
// Standard Deviation
var varianceSum = 0;
for (var i = 0; i < dataPoints.length; i++) {
varianceSum += Math.pow(dataPoints[i] – mean, 2);
}
var variance = varianceSum / (dataPoints.length – 1);
var stdDev = Math.sqrt(variance);
stdDevResultElement.textContent = stdDev.toFixed(4);
}