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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2
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1answer
23 views

Extrapolate data points from a series of averages

Given a series of data points: $$\begin{array}{c|c|c|c|c|c|c|c|} & \text{Monday} & \text{Tuesday} & \text{Wednesday} & \text{Thursday} & \text{Friday} & \text{Saturday} &...
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0answers
35 views

Functions like EWMA

I have a problem in which a threshold triggers an event. I want to estimate that threshold dynamically as I get more information progressively. Exponentially Weighted Mean Average is one such ...
3
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2answers
124 views

Very fascinating probability game about maximising greed?

Two people play a mathematical game. Each person chooses a number between 1 and 100 inclusive, with both numbers revealed at the same time. The person who has a smaller number will keep their number ...
1
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1answer
22 views

Average distance to the closest neighbor

Suppose that 3-dimensional space contains countably infinite number of randomly positioned particles (points), on average $1$ particle per a unit of volume. Their distribution is homogeneous and ...
2
votes
1answer
168 views

How to calculate the average distance between two points in concentric annuli

I tried to solve this analytically but gave up and ran a simulation. I would still like to know if it can be done explicitly. Consider a circle radially divided into 'zones', so say zone 1 is the ...
1
vote
1answer
15 views

Difference between Means is the Mean of the Differences

Suppose you have a sequence $a_{1}, \dots, a_{n}$ and another sequence $b_{1}, \dots, b_{m}$, where $n$ and $m$ may differ. I want to know whether the difference between the arithmetic means of these ...
0
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0answers
38 views

sum of the log over the log of the count (Average of probablities)

I wondering if anyone has seen this "averaging" technique before, and what its advantages might be? The values being averages are probabilities and as such have a value of 1 or less. $\frac{1}{log(n)...
2
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0answers
40 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
0
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1answer
71 views

Interesting Original Probability Question

I have 100 balls, which are all initially yellow. Every minute, I randomly choose a ball and paint it red. How many balls are expected to be red after 100 minutes? Note: I could pick up a ball that's ...
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0answers
41 views

Number of meetings needed for everyone to know everyone

There are 100 people on an island. Each person has an unlimited number of name-tags with his name on it. (Everyone has a different name) When two people meet, each gives the other an unlimited number ...
0
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2answers
55 views

Question about the average number of cycles? [duplicate]

I have 100 cards labelled from 1 to 100. I place this in a row with all the cards face down. On the first turn I flip the first card. Now this card has a number $n$ on it. I then put this card face-up ...
44
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3answers
1k views

Expected number of people to not get shot?

Suppose $n$ gangsters are randomly positioned in a square room such that the positions of any three gangsters do not form an isosceles triangle. At midnight, each gangster shoots the person that is ...
1
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3answers
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
votes
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 ...
0
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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
59 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 ...
0
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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 ...
0
votes
1answer
42 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 ...
1
vote
2answers
43 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
votes
1answer
40 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) ...
1
vote
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 ...
0
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0answers
24 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
votes
0answers
19 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 ...
1
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3answers
87 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 ...
0
votes
1answer
84 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 $...
1
vote
1answer
107 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
votes
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
votes
1answer
161 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
votes
1answer
230 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
votes
1answer
72 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
votes
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 ...
0
votes
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
votes
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 ...
0
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0answers
18 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 ...
1
vote
1answer
54 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'. ...
1
vote
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
39 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
votes
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
59 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
votes
1answer
162 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
vote
1answer
86 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 ...
0
votes
2answers
62 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 ...
0
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2answers
77 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
56 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
122 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
87 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
50 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 ...