Mean Median Mode Calculator

Mean, Median, Mode Calculator

Results:

Mean: –

Median: –

Mode: –

function calculateStatistics() { var inputString = document.getElementById("numberInput").value; var numbers = inputString.split(',').map(function(item) { return parseFloat(item.trim()); }).filter(function(item) { return !isNaN(item); }); if (numbers.length === 0) { document.getElementById("meanResult").innerHTML = "Mean: Please enter valid numbers."; document.getElementById("medianResult").innerHTML = "Median: -"; document.getElementById("modeResult").innerHTML = "Mode: -"; return; } // Calculate Mean var sum = numbers.reduce(function(a, b) { return a + b; }, 0); var mean = sum / numbers.length; document.getElementById("meanResult").innerHTML = "Mean: " + mean.toFixed(4); // Calculate Median var sortedNumbers = numbers.slice().sort(function(a, b) { return a – b; }); var median; var mid = Math.floor(sortedNumbers.length / 2); if (sortedNumbers.length % 2 === 0) { median = (sortedNumbers[mid – 1] + sortedNumbers[mid]) / 2; } else { median = sortedNumbers[mid]; } document.getElementById("medianResult").innerHTML = "Median: " + median.toFixed(4); // Calculate Mode var frequencyMap = {}; var maxFrequency = 0; var modes = []; for (var i = 0; i maxFrequency) { maxFrequency = frequencyMap[num]; } } for (var key in frequencyMap) { if (frequencyMap[key] === maxFrequency) { modes.push(parseFloat(key)); } } if (modes.length === numbers.length) { // All numbers appear once document.getElementById("modeResult").innerHTML = "Mode: No distinct mode (all numbers appear once)"; } else if (modes.length === 0) { // Should not happen if numbers.length > 0 document.getElementById("modeResult").innerHTML = "Mode: No mode found"; } else { document.getElementById("modeResult").innerHTML = "Mode: " + modes.join(', '); } }

Understanding Mean, Median, and Mode

When analyzing a set of data, three fundamental measures help us understand its central tendency: the Mean, Median, and Mode. Each provides a different perspective on what constitutes a "typical" value within the dataset. This calculator helps you quickly determine these values for any set of numbers you provide.

What is the Mean?

The Mean, often referred to as the average, is calculated by summing all the values in a dataset and then dividing by the total number of values. It's the most commonly used measure of central tendency and is sensitive to outliers (extremely high or low values).

Formula:

Mean = (Sum of all values) / (Number of values)

Example: For the numbers 1, 2, 3, 4, 5

• Sum = 1 + 2 + 3 + 4 + 5 = 15
• Number of values = 5
• Mean = 15 / 5 = 3

If we add an outlier, like 1, 2, 3, 4, 100:

• Sum = 1 + 2 + 3 + 4 + 100 = 110
• Number of values = 5
• Mean = 110 / 5 = 22. Notice how the mean is pulled towards the large outlier.

What is the Median?

The Median is the middle value in a dataset when the values are arranged in ascending or descending order. It's particularly useful when a dataset contains outliers, as it is not affected by them as much as the mean.

How to find the Median:

1. Arrange all the numbers in numerical order.
2. If there is an odd number of values, the median is the middle value.
3. If there is an even number of values, the median is the average of the two middle values.

Example (Odd number of values): For the numbers 1, 2, 3, 4, 5

• Sorted: 1, 2, 3, 4, 5
• Median = 3

Example (Even number of values): For the numbers 1, 2, 3, 4, 5, 6

• Sorted: 1, 2, 3, 4, 5, 6
• Median = (3 + 4) / 2 = 3.5

Using the outlier example: 1, 2, 3, 4, 100

• Sorted: 1, 2, 3, 4, 100
• Median = 3. The median remains robust despite the outlier.

What is the Mode?

The Mode is the value that appears most frequently in a dataset. A dataset can have one mode (unimodal), multiple modes (multimodal), or no mode at all (if all values appear with the same frequency).

How to find the Mode:

1. Count the frequency of each value in the dataset.
2. The value(s) with the highest frequency is/are the mode(s).

Example (Unimodal): For the numbers 1, 2, 2, 3, 4, 5

• Frequencies: 1 (once), 2 (twice), 3 (once), 4 (once), 5 (once)
• Mode = 2

Example (Multimodal): For the numbers 1, 2, 2, 3, 4, 4, 5

• Frequencies: 1 (once), 2 (twice), 3 (once), 4 (twice), 5 (once)
• Modes = 2 and 4

Example (No Mode): For the numbers 1, 2, 3, 4, 5

• Frequencies: 1 (once), 2 (once), 3 (once), 4 (once), 5 (once)
• Mode = No distinct mode (all numbers appear once)

Why are these measures important?

Each measure of central tendency offers unique insights:

• Mean: Provides a good overall average, especially for symmetrically distributed data without extreme outliers. Useful in many statistical analyses.
• Median: A robust measure for skewed data or data with outliers, as it represents the true "middle" value. Often used for income or property value analysis.
• Mode: Identifies the most common item or category. Useful for categorical data or to understand popular choices, like the most frequently purchased product.

By using this calculator, you can quickly compute these essential statistics and gain a better understanding of your numerical data.