Standardavvikelse Kalkylator

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What Is Standard Deviation?

Standard deviation measures how far values typically sit from the mean of a data set. It is written σ when the data is a whole population and s when it is a sample. Unlike variance, it is in the same units as your data, so a standard deviation of 3 kg means something you can picture directly. A small value means the numbers are bunched close to the mean; a large value means they are spread out. This calculator gives you both the population and the sample standard deviation, and the variance they come from.

Formula

There are two versions. They differ only in what you divide by before taking the square root.

Population Standard Deviation

σ = √[ Σ(xᵢ − μ)² / N ]
  • σPopulation standard deviation
  • xᵢEach individual data value
  • μPopulation mean
  • NNumber of values in the population

Sample Standard Deviation

s = √[ Σ(xᵢ − x̄)² / (n − 1) ]
  • sSample standard deviation
  • x̄Sample mean
  • n − 1Degrees of freedom (Bessel's correction)

How to Calculate Standard Deviation Step by Step

  1. Calculate the mean.Add all values and divide by the count.
  2. Find each deviation.Subtract the mean from every value: (xᵢ − x̄).
  3. Square the deviations.Squaring removes the minus signs: (xᵢ − x̄)².
  4. Add the squares.This total is the sum of squares, Σ(xᵢ − x̄)².
  5. Divide.Divide by N for a population or by n − 1 for a sample. The result is the variance.
  6. Take the square root.The square root of the variance is the standard deviation.

Standard Deviation Examples

1Student Test Scores (sample)

Data:72, 85, 90, 68, 95
Solution:Mean = (72 + 85 + 90 + 68 + 95) / 5 = 82. Squared deviations: 100, 9, 64, 196, 169. Sum of squares = 538. Sample variance = 538 / 4 = 134.5.
Answer:Sample standard deviation (s) ≈ 11.60

2Daily Temperatures for One Week's Weekdays (°C, population)

Data:20, 22, 19, 23, 21
Solution:Mean = 21. Squared deviations: 1, 1, 4, 4, 0. Sum of squares = 10. Population variance = 10 / 5 = 2.
Answer:Population standard deviation (σ) ≈ 1.41

3Product Weights (grams, sample)

Data:500, 502, 498, 501, 499
Solution:Mean = 500. Squared deviations: 0, 4, 4, 1, 1. Sum of squares = 10. Sample variance = 10 / 4 = 2.5.
Answer:Sample standard deviation (s) ≈ 1.58

4Monthly Rainfall (mm), both versions

Data:50, 75, 30, 90, 60
Solution:Mean = 61. Deviations: −11, 14, −31, 29, −1. Squared: 121, 196, 961, 841, 1. Sum of squares = 2120. Population variance = 2120 / 5 = 424. Sample variance = 2120 / 4 = 530.
Answer:σ ≈ 20.59 | s ≈ 23.02

5Household Energy Bills ($), both versions

Data:95, 110, 87, 102, 98, 115
Solution:Mean ≈ 101.17. Sum of squares ≈ 518.83. Population variance ≈ 86.47. Sample variance ≈ 103.77.
Answer:σ ≈ 9.30 | s ≈ 10.19

How to Use This Standard Deviation Calculator

Paste or type your numbers and the results update straight away:

  1. Enter your values separated by commas, spaces or line breaks. You can paste a column from a spreadsheet.
  2. Choose Sample if your numbers are drawn from a larger group, or Population if they are the whole group.
  3. Read the standard deviation, variance, mean and the other summary figures.
  4. Open "Show Calculation Steps" to see every deviation and squared deviation, then copy the results if you need them.

What the Calculator Shows You

  • Both the sample and the population result, so you can see the effect of the n − 1 correction.
  • The full working: mean, each deviation, each squared deviation and the sum of squares.
  • The mean, range, sum of squares and coefficient of variation from the same input.
  • A chart of your values with the mean and a ±1 standard deviation band.
  • Calculations run in your browser; your numbers are not sent anywhere.

Where Standard Deviation Is Used

Education

Seeing whether a class's marks are tightly grouped or widely spread.

Finance

Volatility of returns is usually reported as a standard deviation.

Manufacturing

Control charts set their limits a fixed number of standard deviations from the target.

Healthcare research

Results tables report "mean ± SD" for measurements such as blood pressure.

Sport

Comparing how consistent two athletes' times or scores are.

Weather

Describing how much daily temperatures vary around the monthly average.

Common Mistakes When Calculating Standard Deviation

These are the errors that most often lead to a wrong answer:

Using the wrong divisor

Dividing by N when your data is a sample makes the result too small. Use n − 1 unless you really do have every member of the group.

Forgetting to square the deviations

Raw deviations from the mean always add up to zero, so averaging them tells you nothing.

Forgetting the square root

If your answer is in squared units, you have calculated the variance, not the standard deviation.

Mixing units

Values recorded partly in centimetres and partly in metres give a meaningless result. Convert everything first.

Rounding too early

Rounding the mean before computing deviations introduces errors that grow through the calculation. Keep full precision until the end.

Standard Deviation or Variance: Which Should You Report?

They describe the same spread. The right one depends on who will read it and what happens next.

For people reading the result, use standard deviation

It is in the same units as the data. "The average is 50 ± 5 kg" is easy to picture; "the variance is 25 kg²" is not.

For further calculation, use variance

Variances of independent quantities add: Var(X + Y) = Var(X) + Var(Y). Standard deviations do not, which is why ANOVA and regression work with variances.

For the 68–95–99.7 rule, use standard deviation

For roughly normal data, about 68% of values fall within one standard deviation of the mean, 95% within two and 99.7% within three.

Converting is one step

Variance = SD². SD = √variance. You never need to recalculate from the raw data to switch between them.

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Vanliga Frågor: Standardavvikelse Kalkylator

Allt du behöver veta om varians.

Vad är standardavvikelsen för 1, 2, 3, 4, 5?

Standardavvikelsen 1, 2, 3, 4, 5 beräknas enligt följande. Medelvärde = 3. Kvadratavvikelser: 4, 1, 0, 1, 4. Summan av kvadrater = 10. Befolkningsstandardavvikelse (σ) = √(10/5) = √2 ≈ 1,414. Sample standardavvikelse (s) = √(10/4) = √2,5 ≈ 1,581. Använd population SD om dessa är alla dina datapunkter; använd prov SD om de representerar ett urval från en större grupp.

Hur beräknar man standardavvikelsen steg för steg?

Så här beräknar du standardavvikelsen steg för steg: 1. Hitta medelvärdet (genomsnittet) av din datamängd. 2. Subtrahera medelvärdet från varje värde för att få avvikelser. 3. Kvadrera varje avvikelse. 4. Hitta medelvärdet av kvadrerade avvikelser (dividera med n för population, n−1 för urval). Detta ger dig variansen. 5. Ta kvadratroten av variansen. Resultatet är standardavvikelsen. Vår kalkylator visar varje steg automatiskt.

Vad är skillnaden mellan standardavvikelse och varians?

Standardavvikelse är kvadratroten av variansen. Variansmått spridda i kvadratiska enheter, medan standardavvikelsen konverterar den tillbaka till de ursprungliga enheterna i dina data. Till exempel, om din data är i meter, är variansen i meter², men standardavvikelsen är i meter. Standardavvikelse är i allmänhet lättare att tolka eftersom den använder samma skala som rådata.

Hur beräknar man standardavvikelsen i Excel?

I Excel använder du STDEV.S(intervall) för provstandardavvikelse och STDEV.P(intervall) för populationsstandardavvikelse. Exempel: =STDEV.S(A1:A10). I Google Sheets fungerar samma funktioner. I Python, använd np.std(data, ddof=1) för exempel SD. I R returnerar sd(x) exempel på standardavvikelse som standard.

Vad är en bra standardavvikelse?

Det finns ingen allmänt "bra" standardavvikelse - det beror på sammanhanget. En låg standardavvikelse innebär att datapunkter samlas tätt runt medelvärdet (mer konsekvent). En hög standardavvikelse betyder att data är mycket spridd (mer varierande). Vid kvalitetskontroll är låg SD att föredra för konsekvens. Vid investeringar indikerar högre SD mer risk. Använd variationskoefficienten (CV) för att jämföra spridning över datauppsättningar med olika skalor.

Kan standardavvikelsen vara negativ?

Nej, standardavvikelse kan aldrig vara negativ. Det är kvadratroten av variansen, och variansen är alltid noll eller positiv (eftersom den summerar skillnader i kvadrat). En standardavvikelse på 0 betyder att alla värden är identiska. Varje spridning i data ger en positiv standardavvikelse.

Should I report the standard deviation or the variance?

Report the standard deviation when people need to read the result, because it is in the same units as the data ("heights vary by about 2.5 inches"). Use the variance when you are doing further maths with it: in ANOVA and regression, and when combining independent variables, variances add but standard deviations do not.

Can the standard deviation be larger than the variance?

Yes, whenever the variance is between 0 and 1. For a variance of 0.25 the standard deviation is √0.25 = 0.5, which is larger. They are equal at 1 (and at 0), and for any variance above 1 the standard deviation is smaller, e.g. variance 4 gives SD 2.