# thesIt

• #### Arif 12:19:08 pm on August 22, 2010 | 0 | # | Tags: basic, error, residual error, statistical error, wikipedia

If we assume a normally distributed population with mean μ and standard deviation σ, and take sample

$x_{1}, x_{2},..., x_{n}\sim N(\mu,\sigma^{2})$

statistical error is then
$\varepsilon_{i}=x_{i}-\mu$

## Residual

while residual is
$\hat{\varepsilon}_{i}=x_{i}-\bar{x}$

hat over the letter ε indicates an observable estimate of an unobservable quantity called ε.

• #### Arif 07:29:29 am on August 22, 2010 | 0 | # | Tags: basic, boxplot, outlier

Drawing boxplot from the following data, whiskers are determined from 1.5 IQR

 no datum drawn as 1 0.026 outlier 2 0.048 whisker low 3 0.070 Q1 4 0.072 5 0.076 Q2 6 0.084 7 0.086 8 0.099 Q3 9 0.102 10 0.103 whisker high

## Outlier

0.026 becomes outlier because 1.5IQR boundary (IQR = Q3 – Q1 = 0.02908) for the lower boundary is Q1 -1.5IQR = 0.0404, hence whisker is 0.048 which is more close to the box inside making 0.026 outlier.

boxplot-basic-concept-example.png

• #### Arif 06:43:00 am on August 22, 2010 | 0 | # | Tags: basic, viscosity, wikipedia

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress.

The cgs physical unit for dynamic viscosity is the poise (P), more commonly expressed, particularly in ASTM standards, as centipoise (cP)

• #### Arif 06:32:12 am on August 22, 2010 | 0 | # | Tags: basic, density, wikipedia

Density of a material is defined as its mass per unit volume.
ρ (in some countries i.e. USA) is also defined as weight per unit volume
Units: (kg/m³), g/cm³

• #### Arif 10:27:38 pm on June 28, 2010 | 0 | # | Tags: basic, standard deviation, statistics, variance

Easiest description for standard deviation definition is distance from mean (expected value) as shown in this graphical depiction

where all the values fall at σ distance within the dotted circle radius. Of course a more real-life situation is shown as

where σ is the square root of the following mean
$\sigma^2 =\frac{\sum_{i=1}^{n}{\sigma_{i}^2}}{n}$

σ² a.k.a. variance is averaged quadratic distances. Explanation:

Distance may have several concepts, in this variance description, distance shows “how far” a value is from its population expected value (mean). Quadratic form of this “how far” is

$\sigma_i=(x_i-\bar{x} )^2$

• #### Arif 10:56:17 am on February 27, 2010 | 0 | # | Tags: basic, pH, wikipedia

pH is a measure of the acidity or basicity of a solution, defined as minus the decimal logarithm of the hydrogen ion activity in a solution.

$pH=- log_{10} (a_{H^{+}})$

common pH scale (can't find where water is?)

• #### Arif 12:39:21 pm on February 21, 2010 | 0 | # | Tags: basic, viscosity, wikipedia

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensional stress. In everyday terms (and for fluids only), viscosity is “thickness”. Thus, water is “thin”, having a lower viscosity, while honey is “thick”, having a higher viscosity.

Viscosity describes a fluid’s internal resistance to flow and may be thought of as a measure of fluid friction. See Newton’ expression: the constant μ is known as the coefficient of viscosity, the viscosity, the dynamic viscosity, or the Newtonian viscosity.

• #### Arif 02:30:46 pm on February 20, 2010 | 0 | # | Tags: basic, validation, verification

Verification: Is the product being built right?
Validation: Is the right product being built?

• #### Arif 11:49:55 am on February 19, 2010 | 0 | # | Tags: basic, interfacial tension, spinning drop, tensiometer, wikipedia

Spinning drop method (rotating drop method) is one of the methods that is used to measure interfacial tension. Basically, measurements are carried out in a rotating horizontal tube which contains a dense fluid. One drop of a less dense liquid is placed inside the fluid.

Since the rotation of the horizontal tube creates a centrifugal force towards the tube walls, the liquid drop starts to be elongated and this elongation stops when the interfacial tension and centrifugal forces are balanced. Values obtained at this equilibrium point are used to estimate surface tension of the particular liquid by using appropriate correlations. A device called “spinning drop tensiometer” is generally utilized for this purpose.

• #### Arif 12:22:45 pm on February 17, 2010 | 0 | # | Tags: basic, interfacial tension, wikipedia, Young-Laplace

osculating circle

radius of curvature of a curve at a point is the radius of the osculating circle at that point.

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