Statistics Calculator

Enter numbers separated by commas or spaces. Press Calculate. The full results panel shows: central tendency (mean, median, mode), position (min, max, range, midrange), spread (pop SD, sample SD, pop var, sample var), percentiles (Q1, Q2, Q3, IQR), shape (skewness, kurtosis), and quality (CV%, outliers). A histogram renders automatically.

Mean = arithmetic average — influenced by outliers. Median = middle value — resistant to outliers. Mode = most frequent — can be absent or multiple. If mean > median, the data is right-skewed (pulled by high values). If mean < median, left-skewed. Example: income data typically has mean $65k but median $45k due to a few very high earners.

Range = max−min (sensitive to outliers). IQR = Q3−Q1 (robust, covers middle 50%). SD = typical deviation from mean (sensitive to outliers). CV% = SD/mean×100 (unit-free comparison). For skewed data: use IQR as the primary spread measure. For symmetric data: use SD. The calculator shows all four simultaneously.

Enter value in the first column, count (frequency) in the second. Click Add Row for additional entries. Example: 25 students scored 70(×5), 80(×12), 90(×8). The calculator computes all statistics as if every individual score were listed. Mean = (70×5+80×12+90×8)/25 = 83.6. Full descriptive statistics follow.

Skewness near 0 = symmetric. Positive skewness: right tail, common in income and price data. Negative skewness: left tail, common in time-to-failure data. Excess kurtosis near 0 = normal-like tails. Positive kurtosis = heavy tails (more extreme values). Financial returns often have high positive kurtosis (fat tails), making extreme events more likely than a normal distribution predicts.

Enter numbers separated by commas or spaces. Press Calculate. Results: count, sum, mean, median, mode, min, max, range, midrange, population SD, sample SD, population variance, sample variance, Q1, Q2, Q3, IQR, skewness, kurtosis, CV%, SEM, geometric mean, RMS, and outliers. A histogram renders automatically for visual distribution.

Central tendency: mean (sensitive to outliers), median (resistant), mode (most frequent). Spread: SD (typical deviation), IQR (middle 50%), range (full span). Compare mean and median — if they differ by more than 10%, data is skewed and median is the better typical value. CV% = SD/mean×100 enables cross-dataset comparison of variability.

Enter each unique value and its frequency count instead of listing every individual value. Example: 25 students — 5 scored 70, 12 scored 80, 8 scored 90. Enter value 70 freq 5, value 80 freq 12, value 90 freq 8. All statistics compute as if all 25 individual scores were entered. Mean = (70×5+80×12+90×8)/25 = 83.6.

The calculator uses the Tukey method: lower fence = Q1 − 1.5×IQR, upper fence = Q3 + 1.5×IQR. Any value outside these fences is listed as an outlier at the bottom of the results. Example: dataset 2,3,4,5,6,100 — value 100 is flagged. Outliers should be investigated (data entry error? genuine extreme case?) before excluding.

Skewness near 0: symmetric. Positive: right tail (mean > median). Negative: left tail (mean < median). |skewness| > 1 is meaningful skew. Excess kurtosis near 0: normal-like tails. Positive kurtosis: heavy tails (fat tails, more extreme events). Financial returns often have positive kurtosis, making extreme events more likely than a normal distribution predicts.