Paste a list of numbers and select sample or population scope to calculate count, mean, squared deviations, variance and standard deviation. Expand the steps table to inspect the first 50 observations; all observations contribute to the final result, including repeats.
Use it to describe the spread of measurements in the same unit. Sample mode estimates population variance from a sample; population mode treats the supplied values as the complete population of interest. To standardize a value see z-score. The P-value tool has separate test assumptions.
Separate numbers with commas, spaces, semicolons or line breaks. Use dot decimals: 1,5 means two values, not 1.5. Negative numbers, zero and scientific notation such as 1e3 are accepted. Limit: 10000 values and 200000 characters. Every value must be finite with absolute magnitude at most 1e100. Unit suffixes, currency symbols, thousands grouping and missing-value labels are rejected.
Mean=Σx/n. Squared deviations=Σ(x−mean)². Population variance=squared deviations/n. Sample variance=squared deviations/(n−1). Standard deviation is the square root of variance. Sample mode needs at least two values. A one-value population has zero variance and standard deviation.
For 2, 4, 6: count=3, mean=4, deviations=−2, 0, 2, squared deviations=4, 0, 4, and total=8. Population variance=8/3≈2.66666667 and standard deviation≈1.63299316. Sample variance=8/2=4 and standard deviation=2. Try example selects sample mode; changing scope clears the result until recalculated.
總體方差除以 n，樣本方差除以 n−1；標準差是方差的平方根。
樣本標準差至少需要兩個數值。
步驟表僅顯示前 50 項，結果使用全部輸入。
明確樣本或總體口徑，衡量數據離散程度。