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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11 views

Approximate values from point groupings

Say I am given a set of values: \begin{bmatrix}0.9&1.1&1&1.95&2&2.05&2.95&2.95&3.1&3\end{bmatrix} Is there a way I can get the 'center' or 'average' values 1, 2, ...
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0answers
7 views

Multiple server queuing model

I have come across the following problem in one of my courses: Let's suppose a patient in a hospital is waiting to be picked by one of the two doctors available. The time till a new pacient arrives ...
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2answers
15 views

Using double integration to compute an average yields a different result than computing it without integration

I'm self-learning multivariable calculus and am using double integration to compute the average value of $f(x,y)$ over some region. I'm trying to solve the following simple problem using two different ...
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1answer
12 views

Generalizing exponential moving average to n samples

Assume that we have a moving average like this: $E_t = a*S_{t-1}+(1-a)*E_{t-1}$ where $E$ would be an estimate we are interested in, and $S$ is a sample we take at each point in time. Now, if we ...
1
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0answers
26 views

Averaging speeds

I read the answer to this question: http://stackoverflow.com/questions/34794664/how-should-i-calculate-the-average-speed-by-road-segment-for-multiple-segments/34795821#34795821 Can anyone please ...
0
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2answers
22 views

Find the percent of boys and girls

I have a basic school academic question which despite of trying very hard I was unable to find a solution - Average score of girls is an exam is $67$ and that of boys is $62$. Find the percentage of ...
1
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3answers
33 views

Number of Likes and Dislikes to Star Rating system

I have a 5 star rating system that outputs a recommendation. A user inputs a rating based on a Like or Dislike. What I would like to know is how to convert the number of likes and dislikes into a ...
0
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0answers
8 views

Weighted average of unit vectors

I am trying to determine the yaw (z) axis of a vehicle given a bunch of sensors, each of them subject to different kinds of error. This means I get a bunch of unit vectors for the z axis, expressed ...
0
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1answer
20 views

Calculating a weighted average for different pay rates and different hours.

I'm trying to take the money earned over several days - each with unique hours worked and dollars earned per hour (hrs and $/hr). What I've done is multiply each days' # of hours by its rate to get ...
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1answer
31 views

Average velocity question? [duplicate]

I usually know how to do these but this one gives me trouble. If a ball is thrown into the air with a velocity of 46 ft/s, its height in feet t seconds later is given by $y = 46t − 16t_{2}$. (a) ...
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1answer
160 views

New Average with a number deleted

A set of consecutive integers were written down: $1, 2, 3, 4, 5, ... x-1, x, x+1, ... n-2, n-1, n$ One number, $x$, is deleted. The arithmetic mean of the remaining numbers is $602/17$. What does ...
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1answer
25 views

If I subtract a number (from a sequence) from the average of all the numbers in that sequence - what do I have?

If I have a number (from a sequence) and I then subtract that number from the average of that sequence- what do I have? I would describe it as a 'deviation from the average' - but is there a better ...
0
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1answer
9 views

Weighted Averages from the world of GMAT..

I am really confused about how this question has been solved. I've given the question, author's approach and then mine. Can you help me figure out why/ why not I have gone wrong? Thanks in advance, ...
0
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1answer
65 views

How can I average two integers digit by digit?

I would like to take two integers of similar size (about the same number of digits) and average them, without having to first add them, and then divide the result by two. Let's say I have the ...
1
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1answer
22 views

Average case of element comparisons when searching for an element x with a specific probability

I just had a midterm, and unfortunately our professor has stated that he will neither discuss nor post any solutions to the midterm, so I'm posting a question that was on it here in hopes that someone ...
35
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3answers
58k views

Why is an average of an average usually incorrect?

Can someone explain why taking an average of an average usually results in a wrong answer? Is there ever a case where the average of the average can be used correctly? As an example, let's say ...
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0answers
15 views

How to find the best-case and average-case number of comparisons performed by a comparison tree?

So I'm reviewing some material before a midterm tomorrow and I came across this question: ...
2
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1answer
2k 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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1answer
25 views

Specific average calculation [closed]

Suppose I have a set of weighted grades for a subject in high school. Like this: 8.4 (weight: 3), 7.2 (weight: 1), 3.4 (weight: 3). When I loop over that set like ...
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1answer
34 views

For all real a, b, order the averages.

I'm taking a proofs class and the textbook says to do this problem: For all real $ a, b > 0 $, show $ \dfrac{2ab}{a + b} \leq \sqrt{ab} \leq \dfrac{a + b}{2} \leq \sqrt{\dfrac{a^2 + b^2}{2}} $ ...
0
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0answers
31 views

Calculating the average case complexity for finding the maximum number in an array

Algorithm: Given a non empty array with $N$ Numerical values, the algorithm finds the location LOC and the maximum value MAX of the largest element of DATA. Initialize K:= 1, LOC:=1, ...
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0answers
49 views

Working out averages for goals scored per football game

If for example I had a sample set of 11 football games. Of those 11 games, there were a total of 8 goals. So I can work out the average goals per game by ...
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0answers
28 views

Is exponential decay a moving average filter?

I learned that a moving average filter is an FIR filter that gives the average of $N$ previous inputs, like this: $y_n = \sum_{i=0}^{N-1}\frac{x_{n-i}}{N}$ As a simple extension, it might be some ...
1
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1answer
30 views

Given the lengths of two sides of a triangle, is it possible to obtain (sharp) bounds for the average length of the sides of the triangle?

The title says it all. Given the lengths of two sides of a triangle, is it possible to obtain (sharp) bounds for the average length of the sides of the triangle? Let the lengths of two sides of ...
1
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1answer
14 views

What is the difference between the natures of finding average value using secant slope and integral?

To my knowledge, there are two ways of finding average (what average I am not too sure, forgot what my teacher said. But I think it has something to do with the mean value theorem) Say you have a ...
4
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1answer
36 views

What is the name of this type of “average”?

Given two variables $x$ and $y$, $$\frac{2}{1/x + 1/y} $$ looks like some kind of average of $x$ and $y$. Is there a name for it? Where can i look up more information (such as properties) of this ...
28
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4answers
2k views

What is to geometric mean as integration is to arithmetic mean?

The arithmetic mean of $y_i \ldots y_n$ is: $$\frac{1}{n}\sum_{i=1}^n~y_i $$ For a smooth function $f(x)$, we can find the arithmetic mean of $f(x)$ from $x_0$ to $x_1$ by taking $n$ samples and ...
0
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2answers
27 views

Properly average irregular samples into discrete regular ones

Imagine you have a device collecting data at not very regular time intervals. For plotting on graph or further processing, you'll want to turn the samples in regular ones, with constant time ...
1
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1answer
26 views

formula to calculate average quiz score

I'm creating a Quiz web application for an assignment. There is a requirement to show a user the average score for a particular quiz (from pool of all users who have tried it before) upon successfully ...
0
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0answers
40 views

Time series analysis, moving-average model, ARMA model

I'm reading documents about time series analysis, including Autoregressive–moving-average model, Moving average model, Wold's theorem, etc. The notation MA(q) refers to the moving average model of ...
1
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5answers
287 views

Is the point of a shape with the greatest average ray length also the “centroid”?

By a shape I mean one with a enclosed area. One example can be with $x^2+y^2+\sin{4x}+\sin{4y}=4$. I am dealing with implicit relations on a 2-d plane. By the "ray length" I mean the length of the ...
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0answers
32 views

Calculating Average “Productivity”

Let me apologise in advance if my terminology is incorrect or if what seems logical to me is completely nonsensical. I am an analyst without a mathematical background and have tried to self teach off ...
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1answer
19 views

Generate exponential weights (sum of all = 1)

I have $500$ observations and I want to make exponential weighted average of them. I want the weights to be something like $w_i = 0.999^t$ when $t$ is from $1$ to $500$ (num of observations). ...
3
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2answers
107 views

In what sense is the “average” of $sin(x)$ equal to 0?

I think it makes intuitive sense that if a phenomenon is described by simple sinusoidal oscillation, it is "on average" equal to its midrange, but I think I failed in trying to make that statement ...
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1answer
21 views

One number to represent the percent changes of multiple numbers

Question: Is there a way to represent the total percent change of multiple numbers (make it into one number that represents change) that isn't just the percent change between the first and last number ...
0
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0answers
27 views

What type of function is F?

Suppose that $ X= \{(x_1,d_1),(x_2,d_2),...,(x_n,d_n)\}$ where $x_i$ for $i=1,...,n$ are variable and $d_i$ for $i=1,...,n$ have constant values, then we define: $$F(X)= \sum_{i=1}^{n}(\frac{ x_i} ...
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0answers
10 views

Probable minimun of a set having only Maximum, Average and the number of values

I have a data set in which I am given the number of values, the average and the max, how can i work out the probable min value? Thanks
0
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0answers
24 views

Calculating percentage of range of values given total set members and average (review ratings)

Given the total number of members in an unknown data set, with values ranging from a minimum of 1 to a maximum of 5, is it possible to determine the probable percentage of values that fall within a ...
0
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1answer
22 views

Factors that Impact a Weighted Average the Most

I am trying to determine how to calculate the factors that have the most significant impact on a weighted average. For example, let's say I am reviewing the number of patients that responded to a ...
3
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1answer
79 views

What about $\lim_{n\to\infty}\frac{\sum_{k=1}^n s_k\mu(k)}{n}$, for the zeros of Dirichlet eta function $s_k=1+\frac{2\pi k}{\log 2}i$ with $k\geq 1$?

Let for integers $k\geq 1$ the corresponding zeros of Dirichlet eta function of the form $$s_k=1+\frac{2\pi k}{\log 2}i,$$ then we can consider the following puzzle, when we multiply previous ...
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1answer
18 views

Weighted average of multiple angles

This answer has a good approach to calculating the average between multiple angles: simply convert each angle to its unit vector, add them up and convert the resulting sum vector back to an angle. The ...
30
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2answers
2k views

What's the mean of all real numbers?

At first, I had thought the average must be zero, since for every positive number there's an equal magnitude negative number to cancel out the positive number's effect on the average, leaving only ...
1
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2answers
51 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 ...
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4answers
2k views

How to find the total amount from given percentage

I am trying to answer this question from internet for my mathematics practice. ...
8
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3answers
7k views

How to add and subtract values from an average?

Say I have 100 numbers that are averaged: number of values = 100 total sum of values = 2000 mean = 2000 / 100 => 20 If I want to add a value and find out the ...
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3answers
1k views

find new average if removing one element from current average

Ok, so say that I have a current rating average: 3.3/5 Now I want to say to remove a rating of 4. How do I find the new average? Or is this even possible?
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1answer
21 views

What is the proper notation for the “average of the last N elements of a sequence”?

I use sliding window average in my calculations: average for the last N elements and average for the N elements before that. What would be the correct mathematical notation to describe this?
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0answers
1k views

Bar Mean vs Bracket Mean

I know that the standard representation for the average of a data set: $$ \bar{x} = \frac{1}{N} \sum_{i}^N{x_i} $$ I have also ran into an average denoted as $\langle x \rangle$. This notation is ...
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1answer
41 views

Aggregating standard deviation to a summary point

I have a range of data (server performance statistics) is formatted as follows, for each server: ...
0
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1answer
8 views

Finding the measured average angular velocities

Supposed I have a couple rows of data with recorded measured ratios $\omega_f/\omega_i$ and they ask me for the "Average Measured $\omega_f/\omega_i$ " This may seem like a really trivial solution but ...