Mean Median Mode Calculator

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mean median mode calculator
Calculate All (Mean, Median, Mode, Range)Mean OnlyMedian OnlyMode Only
Results:
Enter values above and click Calculate.
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";}if(type==="all"||type==="median"){output+="Median (Middle): "+median+"
";}if(type==="all"||type==="mode"){output+="Mode (Most Frequent): "+modes.join(", ")+"
";}if(type==="all"){output+="Range: "+range+"
";output+="Count (n): "+count+"
";output+="Sorted Data: "+nums.join(", ")+"
";}if(showSteps){output+="
";output+="Step-by-Step:
";output+="1. Sum = "+sum+"
";output+="2. Count = "+count+"
";output+="3. Mean = "+sum+"/"+count+" = "+mean.toFixed(4)+"
";output+="4. Sorted list for median: "+nums.join(", ")+"
";}answerDiv.innerHTML=output;}

Calculator Use

This mean median mode calculator is a versatile tool designed to help you analyze sets of numbers quickly and accurately. Whether you are a student working on statistics homework, a researcher analyzing data trends, or a business professional looking for averages, this tool provides instant results for central tendency and dispersion metrics.

By entering your data set, you can find the average (mean), the middle value (median), the most frequent number (mode), and the spread (range) all in one click. You can enter numbers separated by commas, spaces, or even new lines.

Data Input
The raw list of numbers you wish to analyze. The calculator automatically filters out non-numeric characters.
Calculation Type
Choose whether you want a full statistical summary or just a specific metric like the mean or median.
Show Solution Steps
Enable this option to see the mathematical breakdown, including the sum of values and the sorted order of the data set.

How It Works

The mean median mode calculator uses standard statistical formulas to process your input. Understanding these formulas is essential for interpreting your data correctly.

1. The Mean (Arithmetic Average)

The mean is calculated by summing all values in the set and dividing by the count of those values.

Mean (x̄) = Σx / n

  • Σx: The sum of all numbers in the data set.
  • n: The total number of data points.

2. The Median

The median is the physical middle of the data set when arranged in order. If the set has an odd number of values, the median is the middle one. If the set is even, it is the average of the two middle values.

3. The Mode

The mode is the value that appears most frequently. A data set can have one mode, multiple modes (bimodal or multimodal), or no mode at all if all numbers appear only once.

Calculation Example

Scenario: A small business owner wants to find the average daily sales for a week. The sales figures are: $100, $150, $100, $200, $250, $300, $350.

Step-by-step solution:

  1. Sort the data: 100, 100, 150, 200, 250, 300, 350
  2. Calculate Mean: (100+100+150+200+250+300+350) / 7 = 1450 / 7 = 207.14
  3. Calculate Median: The 4th value in the sorted list is 200.
  4. Calculate Mode: 100 appears twice; all others appear once. Mode = 100.
  5. Calculate Range: 350 – 100 = 250.

Common Questions

What is the difference between mean and median?

The mean is the calculated average and is sensitive to "outliers" (extremely high or low numbers). The median is the positional middle and is often more accurate for describing data like home prices or salaries where a few high values might skew the average.

Can a data set have two modes?

Yes, if two different numbers both appear with the same maximum frequency, the data set is "bimodal." Our mean median mode calculator will display all modes identified in your input.

How does the range help in statistics?

The range provides a basic measure of variability. A large range suggests high volatility or diversity in the data, while a small range suggests the numbers are very similar to one another.

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