The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.

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85 views

What is the expected value of this random number?

Suppose $a$ is a random number between 0 and 1 and suppose $b$ is a random number $\in (0,1)$ also. What is the expected value of $a^b$? (i.e. If I performed this operation $n$ times, what would be ...
3
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1answer
37 views

Is this some known mathematical concept?

I was thinking about a way to do a "weighted average" (that's what I call it, could be dead wrong) of a variable $x$ defined for a given range $x_1\leq x\leq x_N$, weighted by an always positive ...
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2answers
32 views

A density and the average of i.i.d. random variables following that density

Suppose $X_1,\ldots,X_n$ are i.i.d. continuous random variables with a common density $g$ and support $G=\{x:g(x)>0\}$. Let $$ Y=\frac{1}{n}\sum_{i=1}^nX_i. $$ It seems intuitive that $Y$ should ...
2
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3answers
58 views

Determining the Average number of Attempts before a result occurs (using defined Probabilities)

I'm trying to solve this problem but I'm completely unsure of what sort of concepts/formulas/proofs I need in order to tackle it. I'm just lost on where to start. Here's an example story problem as it ...
1
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3answers
36 views

Averages of Power Sets

I've been studying power sets and thought this was interesting. $\frac{x+y+\frac{x+y}{2}}{3} = \frac{x+y}{2}$ This is if we have a set of 2 elements, x and y, and we get it's powerset, find the ...
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0answers
13 views

Reversing running average smoothing

This website claims to be able to obtain the original 1-hourly measurements of the Singaporean pollution standards index (PSI) signal, published here in the form of a 3-hourly running average signal. ...
0
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2answers
50 views

What is the average velocity of an object between time intervals? Using the derivative.

Here is my work on this problem so far: I know to find the average velocity, I should first find the derivative of the height vs time function. $$f(t)=80-4.9t^2$$ $$f'(t)=-9.8t+C$$ Where do I go ...
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1answer
40 views

Is This a Weighted Average

I would like to know whether a weighted average can be defined as the product of the different values, to the power of their weights? Basically, I have this formula and I have to describe it in one ...
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2answers
42 views

Is it possible to find the mean of more than two points on a number line?

I know you can find the mean of two points on a number line, just as you can find the mean of two numbers. However, I would like to know, is it possible to find the mean of THREE or more points on a ...
0
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1answer
39 views

Shop keeper mixes 3 varieties of wheat?

A shop keeper mixes 3 varieties of wheat costing ₹12, ₹14 and ₹17 per kg. Which of following represent ratio of mixing of varieties if the mixture is sold at ₹15 per kg and he gains 20% profit ? $ (1) ...
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2answers
26 views

Limit of sequence that depends on another.

I'm a little confused about the following problem: The sequence $a_n$ tends to $a$. Show that $b_n:=\frac{1}{n+1}(a_0+a_1+\cdots+a_n)$ tends to $a$ aswell. It looks like $b_n$ is simply the average ...
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0answers
23 views

Finding the weighted mean with varying errors

Simply enough, I've a set of numbers with varying errors: 2.02 +- 0.10 , 2.26 +-0.30 , 3.24 +- 0.30 , 3.33 +- 0.30 , 3.92 +- 0.30 , 4.02 +- 0.10 I'm certain there's a simple formula to compute the ...
0
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0answers
18 views

Averaging percentages of events occuring

You have $8$ possible events that could occur in a given day. Out of $21$days, only one event occurred once, two and three events occurred $9$ times each, four events occurred once and seven events ...
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3answers
86 views

Difference between these two standard deviation formulas?

Today I started reading statistics and I came across these two S.D formulas: $$\sqrt{\frac 1 n \sum (X - \overline X)^2} \textrm{ and } \sqrt{\frac 1 {n-1}\sum (X - \overline X)^2}$$ What is the ...
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1answer
78 views

Can the norm of a convex combination of vectors be greater than the norm of their sum?

Can the norm of a convex combination of vectors be greater than the norm of their sum? Or is it always the case that: $|| \sum_i w_i x_i || \leq \sum_i w_i \;|| \sum_i x_i || $ (for positive $...
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1answer
101 views

Average difference between consecutive data

I have in my head a very simple concept, but it's difficult to search for. I feel like there must be a function for this in statistics, but I have no idea what to look for. I have a 1 dimensional ...
0
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0answers
11 views

Dividing a segment into intervals. [duplicate]

I want to divide a segment of unit length into three intervals by selecting two distinct arbitrary points on the line segment. If I do this, what is the expected value of the smallest/shortest segment?...
0
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1answer
157 views

How to calculate the average x-coordinate of a region?

I have a region in the x-y plane. Now I randomly select a point inside or on the boundary of the region. What is the expected value of the x-coordinate of my point? I.e. If I perform this operation ...
0
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1answer
221 views

Determine “average min and max” of a list of values

I've got a large dataset of about 1,000 values which represent the flex of a finger (higher s more flexed). The data is collected within 10 seconds. During that time the finger will be repeatedly ...
0
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1answer
59 views

Calculating the average of percentages from fields which have a “weight” multiplier applied.

This is for some software I'm writing. I have a number of fields, all of which have a score input which allows a percentage of 0-100. Each field has a "weight" property, which determines its ...
0
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2answers
32 views

Define temperature by clustering with math operators

I can´t figure out how to cluster the temperature for the weather in 3 optimal cases: hot, mild, cold My data contains: air temperature(the average daily value), max air temperature(highest daily ...
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0answers
28 views

Finding average as well as impact of quantity

I am new to this site, I am basically a developer and stuck at a logical mathematics portion. I have polarity of people sending email, so suppose p1 sent mail and mathematical polarity came out to be ...
2
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1answer
77 views

Average of a list of numbers, read one at a time

I have a dilemma Lets take the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ If we wanted to calculate the average of this set we would add up all the numbers in the set $(45)$ and then divide by the total ...
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0answers
17 views

How can I calculate percent error with a denominator of 0? [duplicate]

I am using the MAPE formula, ABS(actual-forecast)/actual *100, but this raises problems when the actual values are zero. Is it possible to add 1 to the denominator and calculate this way? Would I get ...
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1answer
53 views

Could someone explain the notation of the average of quaternions equation?

The equation has some notation that is difficult to find the meaning for. It is equation (3) in the paper 'Quaternion Averaging' by F. Landis Markley, et al. on page 3 under 'The Average Quaternion'. ...
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1answer
48 views

Why this process is nonergodic?

I am studying a tutorial on stochastic processes and there's an example in it which I don't understand anything of it. First of all there is this criterion for a mean-ergodic random process: For ...
2
votes
1answer
38 views

Is tossing a die in 10 consequent days an ergodic process?

IT maybe an elementary question but I'm totally new to the concept. In Wikipedia, ergodicity is defined as follows: In statistics, the term describes a random process for which the time ...
0
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1answer
42 views

what's the difference between variable and process from a statistical point of view?

I'm reading a tutorial stochastic process: ergodicity and temporal averages and I'm totally confused. It is said that: Suppose an IID random process whose marginal PDF is Gaussian with mean ...
0
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0answers
58 views

what is the difference between statiscal averagre and average?

I'm reading a book on synthetic aperture radar and it is said that: The term $\sigma^{\circ}$ is the averaged radar cross section per unit area, also called the scattering coefficient or ...
0
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1answer
145 views

Combining percentages differences

I would like to know the difference between two approaches of combining percentages. I found an online example that match my situation; the example have been found in The University of Georgia page. ...
1
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1answer
84 views

How to summarize a big table of results? Average or Geometric mean?

I am writing a paper for a Computer Science conference and I have a big (way too big) table of results (times and some other measures) for different versions of an algorithm. I would like to summarize ...
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2answers
60 views

Average value of distinct combinations

Distinct combinations of 123 are 123, 132, 213, 231, 312 & 321. Adding those and dividing by 6 gives the average 222. Same goes for 246: 246, 264, 426, 462, 624 & 642. Added up and divided by ...
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2answers
75 views

Difference between the two ways of finding average winning rate over a period of time

Ok I might be asking something stupid, please bear with me, math is not my strong suit. This has to be a duplicate but I dont know how to search them. I dont even know how to word the title, kindly ...
1
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2answers
54 views

A specific kind of Moving average

The problem is : Consider the list consisting of the first n natural numbers without zero, ie from $1$ to $n$. We define the transformation "moving average" on the list of $n$ elements by ...
4
votes
2answers
131 views

Average $lcm(a,b)$, $ 1\le a \le b \le n$, and asymptotic behavior

What is the average value for $\mathrm{lcm}(a,b)$, with $ 1\le a \le b \le n$, for a given $n$, and what is the asymptotic behavior? The $\mathrm{lcm}$ is the least common multiple. I have ...
0
votes
1answer
117 views

Average score for a Quiz based on recent performance

A quiz always has 10 questions. Correct answer results in 1 mark. No negative marking. A user can take the quiz as many times as he likes. I want to show his 'Average Score' based on last 5 quiz ...
2
votes
1answer
82 views

Why is the average of a sum equal the sum of the averages?

I came across this website showing the proof of the above question in the Expected Value section. However, I do not quite understand why the probability of $xy$ becomes the probability of $x$ (or $y$) ...
0
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1answer
48 views

Intuition: Average vs. Average Rate of Change

I intuitively understand the examples below, but I don't see an "average" in the average rate of change (I see a ratio of two delta values). What is the relationship between the average (arithmetic ...
1
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1answer
12 views

Grading limitless variables

I am trying to calculate the quality of a triangle. Parameters are skewness, aspect ratio, and size. Skewness ranges between 0 and 1. Aspect ratio is the ratio of longest edge to shortest edge. ...
0
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0answers
8 views

How to show monotonicity of this weighted average?

I have a sequence of positive and increasing (in all of its arguments) functions , $\{f_i(x_1, x_2, \dots, x_M)\}_{i=1}^M$. I also have: $$ \Omega_i=\frac{(x_i+f_i(\cdot))^{-1}}{\sum_i(x_i+f_i(\cdot)...
2
votes
2answers
107 views

weighing avg by columns vs rows outputs different results

First of all, I just know the basics of math, so please be patient. I have an overall score for a company with the product1 and product2. However when I do the overall for each criteria like ...
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2answers
41 views

Average Attendance [closed]

I need to find a monthly average attendance. 3 out of 4 weeks were not counted. Do I take the number from the one week that was counted and divide by 4 or just use that one number as the average?
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0answers
35 views

Understanding the convolution as a weighted average to eliminate noise $ s(t) = \int x(a) w(t-a) da$

I was reading Yoshua's Bengio [book][1] on convolutional neural networks and it has small section that described/explains the convolution in the context of estimating the location of a spaceship with ...
3
votes
1answer
48 views

Expected value (mean) of function from polyline

Suppose we have a polyline that has such properties: It consists of n segments First segment's ends are (0, 0) and ...
1
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3answers
43 views

how do they calculate these following columns

I have these data: I am sorry the data is in Portuguese, and it is an image so I can't convert it to a table but the translate "probably" ( i am not a native speakers for Portuguese language) is: ...
0
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0answers
17 views

Moving average where periods have unequal # of samples

I'm trying to compare a simple moving average approach to one that normalizes by the number of samples in a period to determine which is "more correct." Here's a representative piece of the data: <...
0
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1answer
99 views

SAT Math Question Confusion

I was doing a practice new SAT Test and was wondering exactly what this question is asking and how it got to the answer. Thanks!
0
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1answer
75 views

Five-year Annual Average vs five-year Weighted average maintenance costs for two car types

If we are comparing maintenance costs (M$) per mile (M$/m = Mtype) of two car models over a 5 year period, where the number of cars that are type (a) is much less than type (b), and the number of type ...
3
votes
3answers
3k views

what does `ensemble average` mean?

I'm studying this paper and somewhere in the conclusion part is written: "Since this rotation of the coherency matrix is carried out based on the ensemble average of polarimetric scattering ...
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2answers
926 views

Weighted Average Distance between 3 or more points

I'm trying to find out the average point between 3 or more points, given each distance that the end point is away from each of the other points. With 2 points it's easy, I believe the formula should ...