Standard Deviation Calculator
Calculate mean, variance, standard deviation, median, and mode. Supports both population and sample formulas.
About this tool
Standard deviation measures how spread out your data is from the average, making it one of the most important concepts in statistics. While the mean tells you the central tendency, standard deviation reveals the variability—how much individual values typically deviate from that center. This metric is crucial for understanding data consistency, identifying risk in financial portfolios, assessing measurement precision in quality control, and evaluating performance variation in scientific research.
To use the calculator, simply paste or enter your data values (separated by commas or line breaks). Select whether you're analyzing a complete population or a sample from a larger population—this changes the formula because samples tend to show less variation than the full population. The tool instantly computes the mean, variance, standard deviation, median, and mode, giving you a complete statistical snapshot. This is invaluable for researchers validating experimental results, businesses monitoring consistency, educators grading assessments, and analysts interpreting real-world datasets.
Understanding the difference between population and sample standard deviation is key: population SD divides by N, while sample SD divides by N-1 (Bessel's correction) to account for sampling bias. The calculator also displays median and mode, which together with mean provide a robust view of your data's shape and central location. Whether you're analyzing scientific measurements, comparing product quality across batches, or studying variation in test scores, this tool transforms raw numbers into meaningful statistical insights.
Frequently Asked Questions
Code Implementation
import statistics
def full_stats(data, population=True):
"""Calculate comprehensive statistics for a dataset."""
n = len(data)
total = sum(data)
mean = total / n
if population:
variance = sum((x - mean) ** 2 for x in data) / n
else:
variance = sum((x - mean) ** 2 for x in data) / (n - 1)
std_dev = variance ** 0.5
sorted_data = sorted(data)
mid = n // 2
median = (sorted_data[mid - 1] + sorted_data[mid]) / 2 if n % 2 == 0 else sorted_data[mid]
# Mode
from collections import Counter
freq = Counter(data)
max_freq = max(freq.values())
mode = [k for k, v in freq.items() if v == max_freq] if max_freq > 1 else []
cv = (std_dev / abs(mean)) * 100 if mean != 0 else 0
return {
"count": n, "sum": total, "mean": mean,
"variance": variance, "std_dev": std_dev,
"min": sorted_data[0], "max": sorted_data[-1],
"range": sorted_data[-1] - sorted_data[0],
"median": median, "mode": mode,
"cv_pct": cv,
}
data = [4, 8, 15, 16, 23, 42]
result = full_stats(data, population=True)
for k, v in result.items():
print(f"{k:12}: {v}")Comments & Feedback
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