Probable Error Calculator

✖Variable 'b' in Probable Error is the half-range of an interval about a central point for the distribution.ⓘ Variable 'b' in Probable Error [b]			+10% -10%
✖Standard Deviation of the Sample of Size N is the quantity expressed by how much it differs from the mean value for the group and also the square root of its variance.ⓘ Standard Deviation of the Sample of Size N [σ_n-1]			+10% -10%
✖Sample Size is the measure of the number of individual samples to establish the confidence limits.ⓘ Sample Size [N]			+10% -10%

✖Probable Error is the half-range of an interval about a central point for the distribution and in Gumbel's method it defines the range of effective measurement increments.ⓘ Probable Error [S_e]

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Download Gumbel's Method for Prediction of Flood's Peak Formulas PDF PDF Image

Probable Error Solution

STEP 0: Pre-Calculation Summary

Formula Used

Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size))
S_e = b*(σ_n-1/sqrt(N))
This formula uses 1 Functions, 4 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Probable Error - Probable Error is the half-range of an interval about a central point for the distribution and in Gumbel's method it defines the range of effective measurement increments.
Variable 'b' in Probable Error - Variable 'b' in Probable Error is the half-range of an interval about a central point for the distribution.
Standard Deviation of the Sample of Size N - Standard Deviation of the Sample of Size N is the quantity expressed by how much it differs from the mean value for the group and also the square root of its variance.
Sample Size - Sample Size is the measure of the number of individual samples to establish the confidence limits.

STEP 1: Convert Input(s) to Base Unit

Variable 'b' in Probable Error: 8 --> No Conversion Required
Standard Deviation of the Sample of Size N: 1.28 --> No Conversion Required
Sample Size: 2621 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

S_e = b*(σ_n-1/sqrt(N)) --> 8*(1.28/sqrt(2621))

Evaluating ... ...

S_e = 0.200016786781202

STEP 3: Convert Result to Output's Unit

0.200016786781202 --> No Conversion Required

FINAL ANSWER

0.200016786781202 ≈ 0.200017 <-- Probable Error

(Calculation completed in 00.004 seconds)

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< Confidence Limits Calculators

Probable Error

LaTeX Go Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size))

Variate 'b' given Probable Error

LaTeX Go Variable 'b' in Probable Error = Probable Error*sqrt(Sample Size)/Standard Deviation of the Sample of Size N

Sample Size when Probable Error is Considered

LaTeX Go Sample Size = ((Variable 'b' in Probable Error*Standard Deviation of the Sample of Size N)/Probable Error)^2

Equation for Variate 'b' using Frequency Factor

LaTeX Go Variable 'b' in Probable Error = sqrt(1+(1.3*Frequency Factor)+(1.1*Frequency Factor^(2)))

Probable Error Formula

LaTeX Go

Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size))
S_e = b*(σ_n-1/sqrt(N))

What is Flood Frequency Analysis?

Flood frequency analysis is a technique used by hydrologists to predict flow values corresponding to specific return periods or probabilities along a river. The application of statistical frequency curves to floods was first introduced by Gumbel.

What is Peak Discharge?

In Hydrology, the term Peak Discharge stands for the highest concentration of runoff from the basin area. The concentrated flow of the basin greatly exaggerates and overtops the natural or artificial bank, and this might be called a flood.

How to Calculate Probable Error?

Probable Error calculator uses Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size)) to calculate the Probable Error, The Probable Error formula is defined as the correlation coefficient that is fully responsible for the value of the coefficients and their accuracy. Probable Error is denoted by S_e symbol.

How to calculate Probable Error using this online calculator? To use this online calculator for Probable Error, enter Variable 'b' in Probable Error (b), Standard Deviation of the Sample of Size N (σ_n-1) & Sample Size (N) and hit the calculate button. Here is how the Probable Error calculation can be explained with given input values -> 0.109227 = 8*(1.28/sqrt(2621)).

FAQ

What is Probable Error?

The Probable Error formula is defined as the correlation coefficient that is fully responsible for the value of the coefficients and their accuracy and is represented as S_e = b*(σ_n-1/sqrt(N)) or Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size)). Variable 'b' in Probable Error is the half-range of an interval about a central point for the distribution, Standard Deviation of the Sample of Size N is the quantity expressed by how much it differs from the mean value for the group and also the square root of its variance & Sample Size is the measure of the number of individual samples to establish the confidence limits.

How to calculate Probable Error?

The Probable Error formula is defined as the correlation coefficient that is fully responsible for the value of the coefficients and their accuracy is calculated using Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size)). To calculate Probable Error, you need Variable 'b' in Probable Error (b), Standard Deviation of the Sample of Size N (σ_n-1) & Sample Size (N). With our tool, you need to enter the respective value for Variable 'b' in Probable Error, Standard Deviation of the Sample of Size N & Sample Size and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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