| Count (n): | '+n+' |
| Sum: | '+sum.toFixed(4).replace(/\.?0+$/,"")+' |
| Mean (μ): | '+mean.toFixed(4).replace(/\.?0+$/,"")+' |
| Median: | '+median.toFixed(4).replace(/\.?0+$/,"")+' |
| Mode: | '+(modes.length>0?modes.join(", "):"None")+' |
| Range: | '+range.toFixed(4).replace(/\.?0+$/,"")+' |
| Variance ('+(type==='sample'?'s²':'σ²')+'): | '+variance.toFixed(4).replace(/\.?0+$/,"")+' |
| Std. Deviation ('+(type==='sample'?'s':'σ')+'): | '+stdDev.toFixed(4).replace(/\.?0+$/,"")+' |
';out+='1. Sort Data: '+nums.join(", ")+'
';out+='2. Sum: '+sum.toFixed(2)+'
';out+='3. Mean: '+sum.toFixed(2)+' / '+n+' = '+mean.toFixed(4)+'
';out+='4. Sum of Squares: Σ(x – μ)² = '+sqDiffSum.toFixed(4)+'
';if(type==='sample'){out+='5. Sample Variance: '+sqDiffSum.toFixed(4)+' / ('+n+' – 1) = '+variance.toFixed(4);}else{out+='5. Population Variance: '+sqDiffSum.toFixed(4)+' / '+n+' = '+variance.toFixed(4);}out+='
How to Use the Statistics Calculator
The statistics calculator is a versatile tool designed to provide descriptive statistics for any given data set. Whether you are analyzing classroom grades, scientific measurements, or financial trends, this tool handles the heavy lifting of mathematical computation.
To use this calculator, simply follow these steps:
- Data Set Input
- Type or paste your numbers into the text box. You can separate your values using commas, spaces, or new lines.
- Data Type Selection
- Choose "Sample" if your data represents a portion of a larger group. Choose "Population" if you have collected data from every single member of the group you are studying. This choice affects the Variance and Standard Deviation calculations (Bessel's correction).
- Detailed Steps
- Check the "Show detailed calculation steps" box to see the manual process of finding the mean and variance, which is perfect for students double-checking their homework.
Common Statistical Formulas
Our statistics calculator utilizes standard formulas recognized in mathematics and social sciences. Understanding these formulas helps interpret the results more effectively.
The Arithmetic Mean
The mean is the average of the data points. It is calculated by summing all values and dividing by the count.
Mean (μ) = Σx / n
Standard Deviation
Standard deviation measures the dispersion or spread of the data. A low standard deviation indicates that the values tend to be close to the mean, while a high standard deviation indicates that the values are spread out over a wider range.
- Sample Standard Deviation (s): Used when the data is a subset of a population. Uses (n-1) as the divisor.
- Population Standard Deviation (σ): Used when the data is the entire population. Uses (n) as the divisor.
Calculation Example
Example: A small business owner wants to find the average and spread of their daily sales over 5 days: 120, 150, 100, 180, and 200.
Step-by-step solution:
- Sum the values: 120 + 150 + 100 + 180 + 200 = 750
- Calculate Mean: 750 / 5 = 150
- Find Variance (Sample): Sum of squared differences from the mean: [(120-150)² + (150-150)² + (100-150)² + (180-150)² + (200-150)²] = [900 + 0 + 2500 + 900 + 2500] = 6800. Variance = 6800 / (5-1) = 1700.
- Calculate Std. Deviation: √1700 ≈ 41.23
- Results: Mean = 150, Std. Deviation = 41.23
Frequently Asked Questions
What is the difference between Sample and Population?
In statistics, a population includes all members of a defined group, while a sample is a smaller subset of that population. Use "Sample" for almost all real-world experiments unless you have reached every single possible subject in your scope.
Why is the sample standard deviation divided by n-1?
This is known as Bessel's correction. It is used because using the sample mean instead of the true population mean underestimates the variability. Dividing by n-1 provides an unbiased estimate of the population variance.
Can this statistics calculator handle negative numbers?
Yes, the statistics calculator can process negative numbers and decimals. Simply enter them in the data set field as you would any other number.