Statistics Calculator

Inferential & Descriptive Statistical Mathematics

Descriptive statistics summarize the central tendency, dispersion, and distribution shape of numeric datasets.

Primary Statistical Equations

• Arithmetic Mean (Average):

x = (1) / (n) Σ_i=1^n x_i

• Sample Variance (s^2, Bessel's Correction):

s^2 = (1) / (n - 1) Σ_i=1^n (x_i - x)^2

• Sample Standard Deviation (s):

s = √(s^2) = √(Σ (x_i - x))^2n - 1

• Population Standard Deviation (σ):

σ = √((1) / (N) Σ_i=1)^N (x_i - μ)^2

• Interquartile Range (IQR):

IQR = Q_3 - Q_1

• Tukey's Outlier Fences:

Outliers < Q_1 - 1.5(IQR) or Outliers > Q_3 + 1.5(IQR)

How to Use This Calculator

Enter your Enter Dataset (Comma or Space Separated Numbers) (e.g. 12, 45, 67, 34, 89, 23, 56, 78, 45, 34) and Dataset Type (Degrees of Freedom) — choose from Sample Data (n − 1 Bessel's Correction — s, s²), Entire Population (N — σ, σ²). Results update instantly as you type — adjust any value to compare scenarios.

The Formula

Formula Reference: Statistics Calculator

Input variables:

dataSetString — Enter Dataset (Comma or Space Separated Numbers)

calculationTypeSelect — Dataset Type (Degrees of Freedom)

Computed outputs:

meanValue — Mean (Arithmetic Average x̄ / μ)

medianValue — Median (Middle Value Q₂)

standardDeviationValue — Standard Deviation (s / σ)

varianceValue — Variance (s² / σ²)

interquartileRangeIqr — Interquartile Range (IQR)

Mathematical relationships extracted from calculation logic:

sum = nums.reduce((acc, v) => acc + v, 0)

median = nums[Math.floor(n / 2)]

sqDiffSum = nums.reduce((acc, v) => acc + Math.pow(v - mean, 2), 0)

divisor = isSample ? Math.max(1, n - 1) : n

lowerHalf = nums.slice(0, Math.floor(n / 2))

upperHalf = nums.slice(Math.floor(n / 2) + 1)

q3 = upperHalf.length > 0 ? getMedianOfSub(upperHalf) : nums[n - 1]

iqr = q3 - q1

lowerFence = q1 - (1.5 * iqr)

upperFence = q3 + (1.5 * iqr)

Standard: NIST / ISO mathematical definitions

Worked Example

Analyzing 10 test scores (12 to 89) reveals an average of 48.3 with a standard deviation of 25.09, showing wide grade variance around the median of 45.

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Understanding Your Result

Statistical results require context: a mean alone is misleading without knowing the standard deviation (spread). Normal distribution reference: 68% of values fall within ±1 SD of the mean, 95% within ±2 SD, 99.7% within ±3 SD. For small sample sizes (n < 30), use t-distributions rather than z-scores. Statistical significance (p < 0.05) does not imply practical significance — effect size (Cohen's d, R², odds ratio) measures real-world importance. Correlation coefficient r: |r| < 0.3 weak, 0.3–0.7 moderate, > 0.7 strong.