What is Arithmetic mean: Definition and 21 Discussions
In mathematics and statistics, the arithmetic mean ( , stress on first and third syllables of "arithmetic"), or simply the mean or the average (when the context is clear), is the sum of a collection of numbers divided by the count of numbers in the collection. The collection is often a set of results of an experiment or an observational study, or frequently a set of results from a survey. The term "arithmetic mean" is preferred in some contexts in mathematics and statistics, because it helps distinguish it from other means, such as the geometric mean and the harmonic mean.
In addition to mathematics and statistics, the arithmetic mean is used frequently in many diverse fields such as economics, anthropology and history, and it is used in almost every academic field to some extent. For example, per capita income is the arithmetic average income of a nation's population.
While the arithmetic mean is often used to report central tendencies, it is not a robust statistic, meaning that it is greatly influenced by outliers (values that are very much larger or smaller than most of the values). For skewed distributions, such as the distribution of income for which a few people's incomes are substantially greater than most people's, the arithmetic mean may not coincide with one's notion of "middle", and robust statistics, such as the median, may provide better description of central tendency.
So I was thinking about arithmetic, geometric and harmonic means when I had a thought. Let's say we have a curve y = x^2. We want to find the AM of the points on the curve between x=1 and x=2 i.e. y = 1 and y = 4. To make thing easier, we'll start with just the endpoints and keep adding...
Calculation of probability with arithmetic mean of random variables
There are 4 people, each of whom has one deck of cards with 500 cards that are numbered from 1 to 500 with no duplicates.
Each person draws a card from his deck and I would like to calculate the probability of the event that...
The Beer-Lambert law gives the intensity of monochromatic light as a function of depth ##z## in the form of an exponential attenuation:
$$I(z)=I_{0}e^{-\gamma z},$$
where ##\gamma## is the wavelength-dependent attenuation coefficient.
However, if two different wavelengths are present...
Homework Statement
The problem is stated as follows:
"The result in Problem 1-7 has an important generalization: If ##a_1,...,a_n≥0##, then the "arithmetic mean" ##A_n=\frac {a_1+...+a_n} {n}##
and "geometric mean"
##G_n=\sqrt[n] {a_1...a_n}##
Satisfy
##G_n≤A_n##
Suppose that ##a_1\lt A_n##...
Given two positive numbers a and b, we define the geometric mean and the arithmetic mean as follows
G. M. = sqrt{ab}
A. M. = (a + b)/2
If a = 1 and b = 2, which is larger, G. M. or A. M. ?
G. M. = sqrt{1•2}
G. M. = sqrt{2}
A. M. = (1 + 2)/2
A. M = 3/2
Conclusion: G. M. > A. M.
Correct...
Hi.
Let's say I have data which I have measured. For example I measured a length of an object and the measurment was repeated 5 times. An instrument which I used to measure has an error, value of which I know.
My options are to either to just go with the instrument error (probably not, right?)...
Hi everybody, I was doing one asignment form class, I was tasked to prove that in one system, the arimetic mean of FD and BE distributions is equal to MB's distribution for undishtingable particles.
After doing the numbers I found out that it actually was, but I don't know why this happens, can...
Why is the geometric mean used to define the center frequency of a bandpass filter instead of the arithmetic mean?
I read in this book that
1. All the lowpass elements yield LC pairs that resonate at ω = 1.
2. Any point of the lowpass response is transformed into a pair of points of the...
Homework Statement
Showing all your working, calculate the arithmetic mean and standard deviation of the number of days lost.
Table shows man days lost to sickness..
Days lost: 1-3 4-6 7-9 10-12 13-15
Frequency 8 7 10 9 6
Homework Equations...
Homework Statement
If four distinct points on the curve y=2x^4+7x^3+3x-5 are collinear, then find the arithmetic mean of x-coordinates of the aforesaid points.
Homework Equations
The Attempt at a Solution
I think that the four points mentioned must be the roots of the equation.
My discrete mathematics book gives the following definition for the pigeonhole principle:
If m objects are distributed into k containers where m > k, then one container must have more than \lfloor\frac{m-1}{k}\rfloor objects.
It then states as a corollary that the arithmetic mean of a set...
Homework Statement
Two consecutive numbers from 1,2,3...n are removed A.M of remaining numbers is 105/4. Find n and those numbers removed .Homework Equations
Answer
n = 50
those numbers are 7 and 8
The Attempt at a Solution
I solved this question like a few weeks ago but now it escaped my...
Homework Statement
prove: lim x_n = L. Then
\lim_{n\to\infty}\frac{x_1+\cdots+x_n}{n}=L
Homework Equations
The Attempt at a Solution
i don't know abolutely. i tried definition
\left|\frac{x_1+\cdots+x_n}{n}-L\right|=\frac{1}{n}\left|(x_1-L)+\cdots+(x_n-L)\right|
Homework Statement
let r_{1}, r_{2}, ... , r_{n} be strictly positive numbers. Suppose an investment of one dollar at the beginning of the year k grows to 1+r_{k} at the end of year k (so that r_{k} is the "return on investment" in year k). Then the value of an investment of one dollar at...
Homework Statement
A question gives the problem find the two arithmetic means between 4 and 19.
The answer is 9 and 14.
Homework Equations
(a1+a2+a3+an)/n
The Attempt at a Solution
Logic would dictate that the arithmetic mean would be adding 4 and 19 then dividing by two. Leaving...
Homework Statement
When finding the arithmetic mean in a system of equations is there any reason why the method that I am using is wrong?
Find the arithmetic mean of x and y in the following set of equations
Homework Equations
3x + 5y = 65 and
7x + 14y = 175
The Attempt at...
Homework Statement
Prove if that if the limit of a_n = c as n approaches infinity, then the limit of o_n = c as n approaches infinity, where o_n is the arithmetic mean (a_1 + ... + a_n)/n
Homework Equations
I can't figure out how to bound it from below.
The Attempt at a Solution...
Hey,
(sin A + sin B + sin C)/3 >= \sqrt[3]{}(sin A*sin B*sin C)
I know this is true by Arithmetic mean always greater than geometric mean...
but is there any other way of proving this?