Mean Calculator

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Mean Calculator
Arithmetic Mean (Average)Geometric MeanHarmonic Mean

(Separate numbers with commas, spaces, or new lines)

Results:
Mean = 0
Enter numbers above and click calculate.
function calculateMean(){var rawData=document.getElementById('data_input').value;var type=document.getElementById('mean_type').value;var showSteps=document.getElementById('steps').checked;var nums=rawData.split(/[,\s\n]+/).filter(function(x){return x.length>0 && !isNaN(x);}).map(Number);if(nums.length===0){alert('Please enter valid numerical data');return;}var sum=0;var product=1;var harmonicSum=0;var n=nums.length;for(var i=0;i<n;i++){sum+=nums[i];product*=nums[i];harmonicSum+=(1/nums[i]);}var result=0;var stepHtml='';if(type==='arithmetic'){result=sum/n;stepHtml='Step 1: Find the sum of all values.
Sum = '+nums.join(' + ')+' = '+sum.toFixed(4).replace(/\.?0+$/,"")+'

Step 2: Count the number of values.
n = '+n+'

Step 3: Divide Sum by n.
'+sum.toFixed(4).replace(/\.?0+$/,"")+' / '+n+' = '+result.toFixed(4).replace(/\.?0+$/,"");}else if(type==='geometric'){if(product<0 && n%2===0){alert('Geometric mean cannot be calculated for negative products with even roots.');return;}result=Math.pow(product,1/n);stepHtml='Step 1: Multiply all values.
Product = '+product.toFixed(4).replace(/\.?0+$/,"")+'

Step 2: Take the n-th root (n='+n+').
Result = '+result.toFixed(4).replace(/\.?0+$/,"");}else if(type==='harmonic'){if(harmonicSum===0){alert('Harmonic mean error: sum of reciprocals is zero.');return;}result=n/harmonicSum;stepHtml='Step 1: Calculate reciprocal of each value and sum them.
Sum of Reciprocals = '+harmonicSum.toFixed(4).replace(/\.?0+$/,"")+'

Step 2: Divide n by the sum.
'+n+' / '+harmonicSum.toFixed(4).replace(/\.?0+$/,"")+' = '+result.toFixed(4).replace(/\.?0+$/,"");}document.getElementById('meanVal').innerHTML=result.toFixed(4).replace(/\.?0+$/,"");document.getElementById('stepDetails').innerHTML=showSteps?stepHtml:'Solution steps are hidden.';}

Calculator Use

The Mean Calculator is a versatile tool designed to find the central value of a data set. Whether you are a student analyzing test scores, a researcher processing data, or a business owner looking at average sales, this calculator provides instant results for several types of averages.

To use this calculator, simply input your data points separated by commas, spaces, or line breaks. You can select between Arithmetic, Geometric, and Harmonic means depending on your specific mathematical requirements.

Arithmetic Mean
The most common "average," calculated by summing all numbers and dividing by the count.
Data Input
Accepts integers, decimals, and negative numbers. Ensure no text or symbols are included in the data set.
Show Solution Steps
Toggle this option to see the detailed math behind your result, which is helpful for learning or verifying homework.

How It Works

Understanding how to calculate the mean is fundamental to statistics. The process varies slightly based on the type of mean you are seeking:

Arithmetic Mean Formula

x̄ = (Σ xᵢ) / n

  • x̄ (x-bar) represents the arithmetic mean.
  • Σ xᵢ is the sum of all individual data points in the set.
  • n is the total number of data points (the sample size).

Geometric and Harmonic Mean

The Geometric Mean is calculated by multiplying all numbers together and taking the n-th root. It is commonly used in finance to calculate growth rates. The Harmonic Mean is calculated by dividing the total number of values by the sum of the reciprocals of those values, often used for finding average speeds or rates.

Mean Calculation Example

Example: A small business wants to find the average daily revenue over a 5-day work week. The daily revenues are: $120, $150, $100, $180, and $160.

Step-by-step solution:

  1. Sum the values: 120 + 150 + 100 + 180 + 160 = 710
  2. Count the entries: n = 5
  3. Divide the sum by the count: 710 / 5 = 142
  4. Result: The mean daily revenue is $142.

Common Questions

What is the difference between Mean, Median, and Mode?

The mean is the mathematical average. The median is the middle value when the data is sorted in order. The mode is the value that appears most frequently. While the mean is highly sensitive to outliers (extremely high or low values), the median is often a better representation of "typical" data in skewed distributions.

Can the mean be a negative number?

Yes. If the sum of your data points is negative (for example, temperatures in degrees Celsius or financial losses), the arithmetic mean will be negative. However, the geometric mean cannot handle negative numbers if the resulting product would require taking an even root of a negative number.

When should I use the Harmonic Mean?

The harmonic mean is best used when dealing with rates and ratios. A classic example is calculating average speed for a trip. If you drive 60 mph to a destination and 40 mph back, your average speed is the harmonic mean (48 mph), not the arithmetic mean (50 mph).

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