Standard Deviation Calculator

Enter a data set to calculate mean, median, mode, range, variance, and standard deviation (both population and sample).

⚡ Quick Calculator Get a fast estimate

Data Set (comma or space separated)

Statistics for 10 values

σ = 5,549775

Mean (average)

Median

10,5

Mode

No mode

Range

Population Std Dev (σ)

5,549775

Sample Std Dev (s)

5,849976

Population Variance (σ²)

30,8

Sample Variance (s²)

34,222222

Count (n)

Sum

110

Min

Max

Q1 (25th percentile)

Q3 (75th percentile)

IQR (Q3 − Q1)

How to Use

Type or paste your numbers into the input box, separated by commas, spaces, or semicolons. The calculator computes all key statistics including quartiles, variance, and standard deviation.

The Extended Calculator adds a histogram with bell curve overlay, summary stats mode (from n/mean/sd), and a set comparison tool. The Professional Calculator adds confidence intervals, z-score analysis, hypothesis testing, and IQR outlier detection.

Need more detail?

📊 Extended Calculator More options, charts, and scenario comparison

Dataset (comma or space-separated)

Standard Deviation

2.6247

Count

Mean

14.6667

Median

Sample SD

2.7168

Variance (pop)

6.8889

Min / Max

10 / 19

Range

IQR

Bars = frequencyRed curve = normal distributionDashed = mean

Standard Deviation Formulas

Mean (x̄): Σx / n

Population variance (σ²): Σ(x − x̄)² / n

Sample variance (s²): Σ(x − x̄)² / (n − 1) — Bessel's correction

Std deviation: σ = √(σ²) or s = √(s²)

IQR: Q3 − Q1; Outlier fence: Q1 − 1.5×IQR to Q3 + 1.5×IQR

Worked Example

Data: 2, 4, 4, 4, 5, 5, 7, 9

n = 8, Mean = 5

Deviations²: 9, 1, 1, 1, 0, 0, 4, 16 → Sum = 32

Population σ = √(32/8) = 2

Sample s = √(32/7) ≈ 2.14

Need full precision?

🔬 Professional Calculator Complete parameters, sensitivity analysis, and detailed breakdown

Dataset

Confidence Level

95% Confidence Interval

[80.761, 85.506]

Sample mean

83.1333

Sample size

Sample SD

4.6884

Standard Error

1.2105

z-critical (z*)

1.96

Margin of Error

±2.3727

Interpretation: We are 95% confident the true population mean lies between 80.761 and 85.506.

Frequently Asked Questions

Use population std dev (σ) when you have data for the entire population. Use sample std dev (s) when your data is a sample — which covers most real-world situations. Sample divides by (n−1) to correct bias.

Low std dev = data clustered close to the mean (consistent). High std dev = data spread out widely. In finance: high std dev = higher risk/volatility.

Variance is the average of squared deviations. Standard deviation is the square root of variance. Std dev is more useful because it's in the same units as the original data.

For a normal distribution: 68% of data falls within 1 standard deviation of the mean, 95% within 2, and 99.7% within 3 standard deviations.

IQR (Q3 − Q1) measures the middle 50% spread. It's resistant to outliers. Outlier fences: below Q1 − 1.5×IQR or above Q3 + 1.5×IQR flags potential outliers.

Standard Deviation Calculator

How to Use

Standard Deviation Formulas

Worked Example

Frequently Asked Questions

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