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डेटा सेट का मानक विचलन निकालें। जनसंख्या और प्रतिदर्श दोनों की गणना करें।
Sample Standard Deviation
1.581139
Sample Standard Deviation vs Value 1
सूत्र
How to Calculate Standard Deviation
Formula
Population SD (sigma) = sqrt( Sum of (xi - mean)^2 / N )
Sample SD (s) = sqrt( Sum of (xi - mean)^2 / (n - 1) )
Standard deviation is the square root of the variance and is expressed in the same units as the original data. About 68% of data in a normal distribution falls within one standard deviation of the mean.
हल किया गया उदाहरण
Find the standard deviation of 4, 8, 6, 5, 7.
- 01Mean = 30 / 5 = 6
- 02Squared deviations: 4, 4, 0, 1, 1
- 03Sum of squares = 10
- 04Sample SD = sqrt(10 / 4) = sqrt(2.5) ≈ 1.5811
- 05Population SD = sqrt(10 / 5) = sqrt(2) ≈ 1.4142
अक्सर पूछे जाने वाले प्रश्न
What does standard deviation tell you?
It tells you how much individual values typically deviate from the mean. A small SD means values cluster tightly around the mean; a large SD means they are widely spread.
What is the empirical rule?
For approximately normal distributions: ~68% of data falls within 1 SD of the mean, ~95% within 2 SDs, and ~99.7% within 3 SDs.
Can standard deviation be negative?
No. It is the square root of a sum of squared terms, so it is always zero or positive. It equals zero only when all values are identical.
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