Custom Search
Over 10000 Pages Indexed
Your Host
Click here to read about RF CafeKirt
Blattenberger

... single-
handedly
redefining
what an
engineering website
should be.

View the YouTube RF Cafe Intro Video Carpe Diem!
(Seize the Day!)

5CCG (5th MOB):
My USAF radar shop

Hobby & Fun

Airplanes and Rockets:
My personal hobby website

Equine Kingdom:
My daughter Sally's horse
riding business website -
lots of info

•−•  ••−•    −•−•  •−  ••−•  •
RF Cafe Morse Code >Hear It<

Job Board

About RF Cafe©

RF Cafe E-Mail

Averages

As shown in the equations below, there are many different types of averages used in science and mathematics. The one that is probably the most familiar is the Arithmetic Mean.

Arithmetic Mean

To calculate the arithmetic mean with discrete random variables, add up all the terms, and then divide by the number of terms in the distribution. This type of average is commonly called the "average". The mean of a statistical distribution with a continuous random variable is the value of that random variable, formally denoted by the lowercase Greek letter mu (µ). The area under the probability density function curve to the left of µ is the same as the area under the curve to the right of µ (i.e., symmetry).

Arithmetic mean - RF Cafe, n is an integer

Arithmetic Mean Formula


Median

The median of a distribution with discrete random variables where the number of terms is odd then uses the value of the term in the middle. This is the value such that the number of terms having values greater than or equal to it is the same as the number of terms having values less than or equal to it. If the number of terms is even, then the median is the average of the two terms in the middle, such that the number of terms having values greater than or equal to it is the same as the number of terms having values less than or equal to it. The median of a distribution with a continuous random variable is the value m such that the probability is at least 0.5 (50%) that a randomly chosen point on the function will be less than or equal to m, and the probability is at least 0.5 that a randomly chosen point on the function will be greater than or equal to m.

Discrete Random Variable vs. Continuous Random Variable

Since the definitions of Median, Mode, and Range all depend on whether the variables are discrete or continuous, the difference is explained here for clarity. Discrete variables are a countable collection of values, e.g., the numbers 2.2, 5.9, 2.0, 3.4, 6.2, 4.5. There are exactly six values. The mean for them is, per the above formula, 24.2/6 = 4.0(3). The actual result on a calculator is 4.0333333...., but since the precision of all the numbers in the set is two significant figures, the result has to be the same. It has therefore been rounded down to 4.0.

A continuous variable refers to a mathematical function that takes on an infinite number of values between some lower and upper value. For instance, y = x2 [x=14] is the shape of a parabola and is defined for all values of x between 1 and 4. Therefore, y take on an infinite number of values between 1 and 16. Arriving at the answer requires using calculus to divide the integral of the range (x=14, which results in the value of 63) by the range of x (which is 4-1 = 3), to get 63/9 = 7. The precision of the range of x definition is one significant digit, so the answer is the same precision. In this case, even if the range of x was defined as x=1.00000 to x = 4.00000, the answer would still be exactly 7 (7.00000) because the ration 63/9 is exact.

Mode

The mode of a distribution is the value of the term that occurs the most often. Often a distribution will have more than one mode, especially if there are not many terms. This happens when two or more terms occur with equal frequency, and more often than any of the others. A distribution with two modes is called bimodal. A distribution with three modes is called trimodal. The mode of a distribution with a continuous random variable is the maximum value of the function. As with discrete distributions, there may be more than one mode.

Range

The range of a distribution with discrete random variables is the difference between the maximum value and the minimum value. For a distribution with a continuous random variable, the range is the difference between the two extreme points on the distribution curve, where the value of the function falls to zero. For any value outside the range of a distribution, the value of the function is equal to 0.

Weighted Arithmetic Mean

Weighted arithmetic mean - RF Cafe
, n is an integer

Weighted Arithmetic Mean


Geometric Mean

geometric mean

Geometric mean - RF Cafe, n is an integer

Geometric Mean


Harmonic Mean

Harmonic mean - RF Cafe, n is an integer

Harmonic Mean


Root Mean Square (rms)

Root mean square (rms) - RF Cafe n is an integer

Root Mean Square (rms)
A Disruptive Web Presence

Custom Search
Over 10,000 pages indexed! (none duped or pirated)

Read About RF Cafe
Webmaster: Kirt Blattenberger
    KB3UON

RF Cafe Software

RF Cascade Workbook
RF Cascade Workbook is a very extensive system cascaded component Excel workbook that includes the standard Gain, NF, IP2, IP3, Psat calculations, input & output VSWR, noise BW, min/max tolerance, DC power cauculations, graphing of all RF parameters, and has a graphical block diagram tool. An extensive User's Guide is also included. - Only $35.
RF system analysis including
frequency conversion & filters

RF & EE Symbols Word
RF Stencils for Visio

Product & Service Directory
Personally Selected Manufacturers
RF Cafe T-Shirts & Mugs

RF Cafe Software

Calculator Workbook
RF Workbench
Smith Chart™ for Visio
Smith Chart™ for Excel