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Variance (regarding to the arithmetic mean)

The variance measures how far a set of numbers of n equally likely values is spread out. A small variance indicates that the data tend to be very close to ... more

Arithmetic mean size - 1st moment

Calculates the arithmetic mean size (arithmetic method of moments) of the particles’ size distribution of a soil, in metric scale. In statistics, the ... more

Heronian mean

The Heronian mean of two non-negative real numbers is a weighted mean of their arithmetic and geometric means.The weighted mean is similar to an ... more

Arithmetic Mean (in Basic Algebra)

The arithmetic mean (or simply “mean”) of a sample x1,x2,.x3, ... xn is the sum of the sampled values divided by the number of items in the ... more

Harmonic mean

In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average. The harmonic mean is the reciprocal of the ... more

Weighted geometric mean

In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the ... more

Weighted power mean

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... more

Worksheet 341

The awe‐inspiring Great Pyramid of Cheops was built more than 4500 years ago. Its square base, originally 230 m on a side, covered 13.1 acres, and it was 146 m high (H), with a mass of about 7×10^9 kg. (The pyramid’s dimensions are slightly different today due to quarrying and some sagging). Historians estimate that 20,000 workers spent 20 years to construct it, working 12-hour days, 330 days per year.

a) Calculate the gravitational potential energy stored in the pyramid, given its center of mass is at one-fourth its height.

Division
Potential energy

b) Only a fraction of the workers lifted blocks; most were involved in support services such as building ramps, bringing food and water, and hauling blocks to the site. Calculate the efficiency of the workers who did the lifting, assuming there were 1000 of them and they consumed food energy at the rate of 300 Kcal/hour.

first we calculate the number of hours worked per year.

Multiplication

then we calculate the number of hours worked in the 20 years.

Multiplication

Then we calculate the energy consumed in 20 years knowing the energy consumed per hour and the total hours worked in 20 years.

Multiplication
Multiplication

The efficiency is the resulting potential energy divided by the consumed energy.

Division
Generalized mean (power mean)

In mathematics, generalised means are a family of functions for aggregating sets of numbers, that include as special cases the arithmetic, geometric, and ... more

Arithmetic Mean Return

Compound annual growth rate is a business and investing specific term for the geometric progression ratio that provides a constant rate of return over the ... more

Arithmetic Standard Deviation - 2nd moment

Shows how much variation or dispersion from the average exists, on the particles’ size distribution of a soil, in metric scale. Arithmetic mean size (1st ... more

Weighted arithmetic mean

The weighted mean is similar to an arithmetic mean (the most common type of average), where instead of each of the data points contributing equally to the ... more

Estimated Blood Alcohol Concentration - EBAC

Blood alcohol content (BAC), also called blood alcohol concentration, blood ethanol concentration, or blood alcohol level is most ... more

Gamma distribution Mean (With a shape parameter k and a scale parameter θ)

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The parameterization with k ... more

Standard Error

The standard error (SE) is the standard deviation of the sampling distribution of a statistic. The term may also be used to refer to an estimate of that ... more

Division

It is an arithmetic operation.Conceptually, division describes two distinct but related settings. Partitioning involves taking a set of size a and forming ... more

Gamma distribution Mean (With a shape parameter α and a rate parameter β )

In probability theory and statistics, the gamma distribution is a two-parameter family of continuous probability distributions. The parameterization with α ... more

Heinz mean

In probability and statistics, mean and expected value are used synonymously to refer to one measure of the central tendency either of a probability ... more

Standard deviation of any arithmetic progression

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant and is ... more

Bayes estimator - Internet Movie Database (IMDB)

In estimation theory and decision theory, a Bayes estimator or a Bayes action is an estimator or decision rule that minimizes the posterior expected value ... more

Process Capability Index - Cpkm

In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: the ability of a ... more

Process Capability Index - Cpm

In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: the ability of a ... more

Arithmetic progression

An arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant and is ... more

Process Capability Index - Cp,lower

In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: the ability of a ... more

Process Capability Index - Cp,upper

In process improvement efforts, the process capability index or process capability ratio is a statistical measure of process capability: the ability of a ... more

Film temperature

In heat transfer and fluid dynamics, the film temperature is an approximation to the temperature of a fluid inside a convection boundary layer. It is ... more

Cross-multiplication - Rule of Three

In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can ... more

Shockley ideal diode equation

In electronics, a diode is a two-terminal electronic component with asymmetric conductance; it has low (ideally zero) resistance to current in one ... more

Shockley diode equation (small forward bias voltages)

In electronics, a diode is a two-terminal electronic component with asymmetric conductance; it has low (ideally zero) resistance to current in one ... more

Shockley diode equation (in real transistors)

In electronics, a diode is a two-terminal electronic component with asymmetric conductance; it has low (ideally zero) resistance to current in one ... more

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