Toolfix.info

Average Calculator โ€” Mean, Median, Mode & Range Calculator

ToolFix B2B e-commerce and financial calculator dashboard tools illustration


Average Calculator

Calculate Mean, Median, Mode, Range & Standard Deviation


Separate numbers with commas, spaces, or line breaks. Example: 85, 92, 78, 95

โ€”
Mean (Average)
โ€”
Median
โ€”
Mode
โ€”
Range
Countโ€”
Sumโ€”
Minโ€”
Maxโ€”
Std Dev (Population)โ€”
Std Dev (Sample)โ€”
Sorted Data:

โ€”

// Range const range=sorted[n-1]-sorted[0];

// Std Dev const meanDiffSq=nums.map(v=>Math.pow(v-mean,2)); const variance=meanDiffSq.reduce((a,b)=>a+b,0)/n; const stdP=Math.sqrt(variance); const stdS=n>1?Math.sqrt(meanDiffSq.reduce((a,b)=>a+b,0)/(n-1)):0;

document.getElementById('avgMean').innerText=mean.toFixed(2); document.getElementById('avgMedian').innerText=median.toFixed(2); document.getElementById('avgMode').innerText=modeStr; document.getElementById('avgRange').innerText=range.toFixed(2); document.getElementById('avgCount').innerText=n; document.getElementById('avgSum').innerText=sum.toLocaleString(undefined,{maximumFractionDigits:2}); document.getElementById('avgMin').innerText=sorted[0]; document.getElementById('avgMax').innerText=sorted[n-1]; document.getElementById('avgStdP').innerText=stdP.toFixed(4); document.getElementById('avgStdS').innerText=stdS.toFixed(4); document.getElementById('avgSortedVals').innerText=sorted.join(', '); document.getElementById('avgRes').classList.add('active'); }

How to Use the Average Calculator

Enter your numbers in the text box, separated by commas, spaces, or line breaks. Click “Calculate” and the calculator instantly computes:

  • Mean โ€” The arithmetic average (sum รท count)
  • Median โ€” The middle value when sorted
  • Mode โ€” The most frequently occurring value(s)
  • Range โ€” The difference between the largest and smallest values
  • Standard Deviation โ€” Both population (ฯƒ) and sample (s) versions

Mean, Median, and Mode Explained

These are the three most common measures of central tendency in statistics:

  • Mean (Arithmetic Average): Add all numbers together and divide by the count. Formula: Mean = ฮฃx รท n. The mean is sensitive to outliers โ€” one extremely large or small value can skew the average significantly.
  • Median: Sort the numbers from smallest to largest, then find the middle value. If there’s an even number of values, the median is the average of the two middle numbers. The median is more robust against outliers than the mean.
  • Mode: The value that appears most frequently. A dataset can have no mode (all values unique), one mode (unimodal), or multiple modes (bimodal/multimodal).

Practical Examples

Example 1: Class Test Scores

Scores: 85, 92, 78, 95, 88, 90, 72, 85, 93, 87. Mean = 86.5, Median = 87.5, Mode = 85 (appears twice), Range = 95 โˆ’ 72 = 23.

Example 2: Home Prices (Outlier Effect)

Prices: $200K, $220K, $210K, $230K, $1.2M. Mean = $412K (skewed by the mansion), Median = $220K (much more representative). This is why real estate reports use median prices!

Example 3: Standard Deviation

Dataset: 10, 10, 10, 10, 10. Mean = 10, Standard Deviation = 0 (no spread). Dataset: 2, 6, 10, 14, 18. Mean = 10, Standard Deviation โ‰ˆ 5.66 (high spread). Standard deviation measures how spread out the data is from the mean.

Frequently Asked Questions

What is the difference between mean and average?

In everyday language, “average” and “mean” are used interchangeably and refer to the arithmetic mean. However, in statistics, “average” is a broader term that can refer to any central tendency measure including mean, median, and mode. The arithmetic mean is the most commonly used type of average.

When should I use median instead of mean?

Use the median when your data has outliers or is skewed. Common examples include income data (a few very high earners skew the mean), home prices, and response times. The median gives a more representative “middle” value in these cases.

What does standard deviation tell you?

Standard deviation measures how spread out data is from the mean. A low standard deviation means data points cluster close to the mean (consistent). A high standard deviation means data is spread out over a wide range (variable). In a normal distribution, about 68% of data falls within 1 SD, and 95% within 2 SDs.

What is the difference between population and sample standard deviation?

Population standard deviation (ฯƒ) divides by N (total population size). Sample standard deviation (s) divides by N-1 to account for the fact that a sample underestimates variability. Use population SD when you have data for the entire group; use sample SD when working with a subset.