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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1answer
31 views

Average velocity of fluid flow

Washburn equation for fluid flow in horizontal capillary is given by : $\frac{dL}{dt} = \frac{γR}{4µL}$ Find the time dependencies of length of travel, $L(T)$ and average velocity. I can find the ...
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12 views

Weighted rating value

I have a database consisting of clubs and its ratings people have provided them with. Currently, I am performing an average of the ratings based on a club and then sorting these averages ...
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25 views

Which is the default Standard Deviation Formula

I have to implement a test from research paper which says: As for testing criteria, standard deviation or min-to-90th percentile ( ) of large packets (1500 B) can be effectively used to find the ...
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5 views

Graphical Representation of the Risk over different aspects

I am having the Risk Factors which are from more than one assessment. want to show the Risk of the all assessment for year 2015 or any Month of 2015. all risk factors can be the part of any of the ...
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16 views

Calculating Weighted Averages – selecting a correct numerical scale for several variables

I have the following variables that i am going to use to calculate a weighted average: Variable Format Weight applied (out of 1) A Percentage 0.2 B Percentage ...
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2answers
54 views

Finding average of denominator knowing average of numerator and average of fraction [closed]

Good day to you all. I have a little problem I have been banging my head on for a while. I have come to think that it is impossible, but I hope you can save me. I have a fraction, $ ...
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1answer
20 views

Weighted average of household size given number of households of each size

I hope this isn't too simple to bother you with, but this calculation is at the center of a dispute at work and I want to make sure I'm on solid ground here. To begin with, we know that the average ...
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2answers
21 views

Average of two trips

Question While Driving from City A to City B,a car got 22 miles per gallon and while returning on the same road, the car got ...
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1answer
33 views

Is not always the accumulated probability until the expected value equal to 1/2?

My problem is that doing calculations with exponential distribution, the result I get is not 1/2, and I think it should be that according to the intuitive concept of the expected value. The density ...
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1answer
34 views

Determine skewness if only mode and median given?

For a given set of data the mean is 10.5 and the mode is 9. What c an we deduce about the skewness of the data? A The data is positively skewed. B The data is negatively skewed. C ...
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13 views

Potential Reward Average

I'll try to get straight to the point. I'll be offering a reward system as part of a marketing scheme and it will be for a select amount of users who opt-in. What will be calculated is the overall ...
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0answers
17 views

What are the different ways to do a rating in a web application?

I tried to do an example using Bayesian Average in order to find the rating for 3 hotels. Following is my example, Hotel A 3 Votes/ 2 Star/ 1 Star,Rating- 3 Star Hotel B 1 Vote, Rating -5 Star ...
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1answer
17 views

Problem finding the median when using frequency tables

My question concerns finding the median from a frequency table. It only occurs if you have even amounts of data. My problem is this if I had 40 bits of data in a grouped frequency table the middle ...
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1answer
18 views

Unusual Weighted Average Calculation

Unfortunately I don't know the term for what exactly I'm looking for. I hope you guys can direct me. Problem at hand: Have a composite score for an employee performance, for example a score may ...
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1answer
14 views

Finding the average when two infos on averages are given

This is one competitive exam's question. Can someone give me an easy explanation on how to solve this problem? Question Sam earned a $2000 commision on a big ...
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3answers
139 views

Possibility that two students answer the same on a 25 question multiple choice test

I am trying to get some approximation of the possibility that two students would answer $25$ questions in a row exactly the same. There are 4 possible responses for each question. I calculate the ...
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1answer
24 views

Upper bound on an expectation

I'm looking for an upper bound on $E(X^k)$ where $X$ is a random variable with $E(X)=1$. How can I go about doing this?
2
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1answer
19 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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24 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 ...
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2answers
107 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 ...
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1answer
17 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
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1answer
78 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 ...
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1answer
12 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 ...
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35 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. ...
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0answers
34 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 ...
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1answer
69 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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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 ...
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2answers
50 views

Question about the average number of cycles?

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 ...
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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 ...
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72 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 ...
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1answer
36 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
49 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 ...
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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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11 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. ...
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2answers
44 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 ...
0
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1answer
31 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
37 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 ...
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1answer
36 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
25 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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22 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 ...
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0answers
17 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
76 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
47 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
57 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 ...
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0answers
10 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 ...
0
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1answer
64 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
125 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
35 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
31 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 ...