Statistics Calculator

by
Statistics Calculator
Sample Statistics (n-1)Population Statistics (n)
Statistical Results:
Count (n):
Sum:
Mean (μ):
Median:
Mode:
Range:
Variance (s²):
Std Dev (s):
Min:
Max:
function calculateStats(){var input=document.getElementById('data_points').value;var type=document.getElementById('calc_type').value;var cleanInput=input.replace(/[\r\n]/g, ' ').replace(/,/g, ' ');var arr=cleanInput.split(' ').filter(function(v){return v!==" && !isNaN(v);}).map(Number);if(arr.length<2){alert('Please enter at least two numeric values.');return;}arr.sort(function(a,b){return a-b;});var n=arr.length;var sum=0;for(var i=0;i<n;i++){sum+=arr[i];}var mean=sum/n;var sqDiffSum=0;for(var j=0;j<n;j++){sqDiffSum+=Math.pow(arr[j]-mean,2);}var variance=type==='sample'?sqDiffSum/(n-1):sqDiffSum/n;var sd=Math.sqrt(variance);var median;if(n%2===0){median=(arr[n/2-1]+arr[n/2])/2;}else{median=arr[Math.floor(n/2)];}var counts={};var maxFreq=0;var modes=[];for(var k=0;kmaxFreq){maxFreq=counts[num];}}for(var key in counts){if(counts[key]===maxFreq && maxFreq>1){modes.push(key);}}var modeStr=modes.length>0?modes.join(', '):'None';document.getElementById('res_count').innerText=n;document.getElementById('res_sum').innerText=sum.toFixed(4);document.getElementById('res_mean').innerText=mean.toFixed(4);document.getElementById('res_median').innerText=median.toFixed(4);document.getElementById('res_mode').innerText=modeStr;document.getElementById('res_range').innerText=(arr[n-1]-arr[0]).toFixed(4);document.getElementById('res_var').innerText=variance.toFixed(4);document.getElementById('res_sd').innerText=sd.toFixed(4);document.getElementById('res_min').innerText=arr[0];document.getElementById('res_max').innerText=arr[n-1];document.getElementById('answer').style.display='block';}

How to Use the Statistics Calculator

The statistics calculator is a versatile tool designed to provide a comprehensive analysis of a dataset. Whether you are a student working on a classroom assignment or a researcher analyzing raw data, this tool simplifies complex mathematical processes into a few clicks.

To use this calculator, simply enter your numbers into the text area. You can separate your values using commas, spaces, or new lines. Once your data is entered, choose between "Sample" and "Population" statistics and click "Calculate."

Data Input
Enter your raw data points. The calculator handles integers, decimals, and negative numbers.
Sample vs. Population
Choose Sample if your data is a subset of a larger group. Choose Population if you have data for every member of the group you are studying.

Fundamental Formulas Explained

Understanding the math behind the statistics calculator helps in interpreting the results correctly. Below are the primary formulas used in our descriptive statistics engine:

Arithmetic Mean (Average)

μ = (Σx) / n

The mean is the sum of all observations divided by the total number of observations. It represents the central tendency of the data.

Sample Variance

s² = Σ(x – μ)² / (n – 1)

The variance measures how far each number in the set is from the mean. For a sample, we use n-1 (Bessel's correction) to provide an unbiased estimate of the population variance.

Standard Deviation

s = √s²

Standard deviation is the square root of the variance. It is widely used because it is expressed in the same units as the original data.

Statistics Calculation Example

Example: A local bookstore tracks the number of books sold daily over 5 days: 12, 15, 12, 18, 20.

Step-by-step solution:

  1. Sum: 12 + 15 + 12 + 18 + 20 = 77
  2. Mean: 77 / 5 = 15.4
  3. Median: Sorted: 12, 12, 15, 18, 20. Middle value is 15.
  4. Mode: 12 appears most frequently.
  5. Sample Variance: [(12-15.4)² + (15-15.4)² + (12-15.4)² + (18-15.4)² + (20-15.4)²] / (5-1) = 13.3
  6. Std Dev: √13.3 = 3.647

Common Questions

When should I use Sample vs. Population?

Use Population if you have data for every member of the group you are interested in (e.g., all students in a specific classroom). Use Sample if you are taking a small group to represent a larger whole (e.g., surveying 100 people to represent a city of 100,000).

What is the significance of the Median?

The median is less sensitive to outliers (extreme values) than the mean. In datasets with extreme highs or lows (like household income), the median often provides a more realistic "middle" value.

Can there be more than one mode?

Yes. If two values appear with the same maximum frequency, the dataset is "bimodal." If more than two appear, it is "multimodal." If all values appear only once, there is no mode.

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