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Probable Error Formula

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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. Check FAQs

S e = b \cdot (\frac{σ n-1}{\sqrt{N}})

S_e - Probable Error?b - Variable 'b' in Probable Error?σ_n-1 - Standard Deviation of the Sample of Size N?N - Sample Size?

Probable Error Example

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With units

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Here is how the Probable Error equation looks like with Values.

Here is how the Probable Error equation looks like with Units.

Here is how the Probable Error equation looks like.

0.2 = 8 \cdot (\frac{1.28}{\sqrt{2621}})

0.2 = 8 \cdot (\frac{1.28}{\sqrt{2621}})

0.2 = 8 \cdot (\frac{1.28}{\sqrt{2621}})

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Probable Error Solution

Follow our step by step solution on how to calculate Probable Error?

FIRST Step Consider the formula

S e = b \cdot (\frac{σ n-1}{\sqrt{N}})

Next Step Substitute values of Variables

∴

S e = 8 \cdot (\frac{1.28}{\sqrt{2621}})

Next Step Prepare to Evaluate

∴

S e = 8 \cdot (\frac{1.28}{\sqrt{2621}})

Next Step Evaluate

∴

S e = 0.200016786781202

LAST Step Rounding Answer

∴

S e = 0.2

Probable Error Formula Elements

Variables

Functions

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.

Symbol: S_e

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Probable Error

Variable 'b' in Probable Error

Variable 'b' in Probable Error is the half-range of an interval about a central point for the distribution.

Symbol: b

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Variable 'b' in Probable Error

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.

Symbol: σ_n-1

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Standard Deviation of the Sample of Size N

Sample Size

Sample Size is the measure of the number of individual samples to establish the confidence limits.

Symbol: N

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Sample Size

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.

Syntax: sqrt(Number)

Other formulas in Confidence Limits category

Go Sample Size when Probable Error is Considered

N = {(\frac{b \cdot σ n-1}{S e})}^{2}

Go Variate 'b' given Probable Error

b = S e \cdot \frac{\sqrt{N}}{σ n-1}

Go Equation for Variate 'b' using Frequency Factor

b = \sqrt{1 + (1.3 \cdot K z) + (1.1 \cdot {K z}^{2})}

Go Confidence Interval of Variate

x 1 = x T + f c \cdot S e

How to Evaluate Probable Error?

Probable Error evaluator uses Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size)) to evaluate 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 evaluate Probable Error using this online evaluator? To use this online evaluator 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.

FAQs on Probable Error

What is the formula to find Probable Error?

The formula of Probable Error is expressed as Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size)). Here is an example- 0.109227 = 8*(1.28/sqrt(2621)).

How to calculate Probable Error?

With Variable 'b' in Probable Error (b), Standard Deviation of the Sample of Size N (σ_n-1) & Sample Size (N) we can find Probable Error using the formula - Probable Error = Variable 'b' in Probable Error*(Standard Deviation of the Sample of Size N/sqrt(Sample Size)). This formula also uses Square Root (sqrt) function(s).

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Probable Error Formula

Probable Error Example

Probable Error Solution

Probable Error Formula Elements

Other formulas in Confidence Limits category

How to Evaluate Probable Error?

FAQs on Probable Error

Variable Name