StatisticsAnalytics
Descriptive Statistics & Standard Deviation Calculator
Analyze any numeric dataset. Instantly compute mean, median, mode, range, sample & population standard deviation, and variance with sorted data view.
Data Input
Valid data points identified: 9Sum: 784
Descriptive Statistics
Arithmetic Mean (Average):
87.1111
Sample Std Deviation (s):±8.3433
Population Std Dev (σ):±7.8662
Median:88
Mode:85
Minimum - Maximum:72 to 99
Range:27
Mathematical Formula: Sample & Population Standard Deviation
s = √[Σ(x - x̄)² / (n - 1)] | σ = √[Σ(x - μ)² / N]
Measures dispersion of values around the arithmetic mean.
How to Use This Calculator
- 1Paste or type numbers separated by commas, spaces, or line breaks (e.g., 12, 15, 18, 22, 25, 30).
- 2Click Calculate Statistics.
- 3Review complete summary table with count, sum, mean, median, mode, variance, and standard deviations.
Practical Example: Exam Scores Analysis
Scenario: Data: 78, 85, 92, 85, 90, 95
Data:78, 85, 92, 85, 90, 95
Result: Count: 6 | Mean: 87.5 | Median: 87.5 | Mode: 85 | Sample Std Dev (s): 6.12 | Range: 17
Average score is 87.5 with a standard deviation of ±6.12 points.
Frequently Asked Questions
The mean is the mathematical average of all values, while the median is the middle value when numbers are sorted. Median is more resistant to extreme outliers.
Pro Calculation Tips
- Use Sample Standard Deviation (s) when analyzing a sample drawn from a larger population; use Population (σ) when you have every single data point.
Model Assumptions
- Requires at least 2 data points for sample variance (n - 1).