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Questions tagged [average]

Averages summarise a set of values in one way or another. Without further qualification it most commonly refers to the arithmetic mean, but other averages such as root-mean-square exist.

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Proving the median is less than the mean

I was given the following problem by a colleague who is studying for the GRE. The question, I believe, comes from a study guide. A rope is cut into five pieces of differing lengths. After the rope ...
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0answers
33 views

How to convert vectors of unequal length to the same size [on hold]

I have a set of time series vectors that have varying lengths and I am trying to determine a method using which all of them could have the same specified length.
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1answer
42 views

Finding the Elements from a list which average to a Known Number

I apologize as I am very new to this so my question may not be written very well/formally. What I am trying to do is find which numbers out of a known list would average to a given number. Say the ...
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1answer
14 views

Method of selecting the optimal average combination of highest numbers?

I know of pairing functions, but my problem may involve three to five variables. When I have a few robots configured with certain parameters for movement, and I want to evaluate the robots based on ...
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0answers
13 views

Calculate what % an average is of an average of a total of which the values that make up the first average are a part

Situation (example only): I have 10 steps that each have a start and end time, the steps occur in order. I'll refer to the steps as steps 1 through 10. I have between 1 and infinite (inclusive) ...
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1answer
9 views

Simple question about averages and proportions/ratios

I'd like to get the global average of 2 numbers in their proportions. How's that possible? Here is the example of what I want: ...
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0answers
28 views

Formula to predict time to do a number of tasks I can complete per hour if I can complete tasks concurrently.

I am looking to see if there is a specific formula that can predict the amount of time it will take to accomplish a set number of tasks if I can do a certain number of tasks concurrently, based on an ...
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0answers
25 views

Autonomous dynamical system on $\mathbb{R}^2$. Slow decay with superposed but also decaying oscillation.

I am looking at the following autonomous dynamical system $\dot{\mathbf x}(t)=\mathbf{f}(\mathbf{x}(t))$ on $\mathbb R^2$, with $\mathbf x=(x,y)$ $\dot x=-3x\sin(y)^2,$ $\dot y=-\frac{1}{x}-\frac{3}{...
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3answers
39 views

Is weighted average always smaller or equal than arithmetic average?

Is a weighted average, assuming the weights sum up to one, always smaller than the unweighted arithmetic average? As if the weights are smaller than one the weighted mean is a convex combination of ...
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3answers
34 views

Arithmetic mean of error of N coin flips from N/2

When flipping $N$ fair coins, there is obviously an expected output of $\frac{N}{2}$ heads, but there will be some error from that value for individual runs. What I want is the arithmetic mean of ...
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1answer
12 views

How to calculate the success rate against non-occurring events?

I am calculating a football team's success rate ofShots Savedagainst the opposition'sShots On Targetfor every match. It's very ...
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2answers
34 views

How do I find $\bar{y}$ in this question?

A summary of $20$ observations of $y$ gave the following information $\sum(y-a)=-37$ $\sum(y-a)^2=1529$ Find the mean and standard deviation of $y$. In this question, I was able to ...
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1answer
41 views

Writing median rather than mean

I have some code to calculate the mean bias between two arrays. $$mean_{bias}=\frac{\sum_{i=1}^{n}a_i-b_i}{n}$$ and was hoping to represent the median instead: $$median_{bias}=Median(a-b)$$ Does ...
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1answer
20 views

Does anything like expectation of joint distribution exist?

I know how to find the expectation of a function of a Random Variables, I was just wondering that does expectation of a joint distribution exists? I think, since expectation is an average which by ...
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1answer
25 views

Average direction between two vectors

this is my first time asking a question so I'm sorry in advance for any mistake I might make. So I have 3 points in 3D space: A, B and C. What I want to do is have an object on point B point towards ...
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1answer
37 views

How do I calculate the average salary of a data set?

I have been given a dataset and been tasked with calculating the average wage for different job titles. The data includes a mix of ranges (min-max) and values. If we assume for the job title, ...
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1answer
15 views

Mean distance between two points in a square polar coordinates conversion

In this video, around the 5:20 mark, YouTuber MindYourDecisions converts the double integral from rectangular coordinates to polar coordinates so as to make the evaluation easier. However, I fail to ...
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0answers
14 views

number of times an experiment has to be repeated for optimal mean

I am trying to get the total execution time of a program - running it different times will give different run times since it depends on a lot of factors. Thus, I am running this program multiple times ...
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0answers
27 views

How to calculate average between 2 joints?

I have $21$ joints (each joint has $2$ coordinates $(x,y)$). I would like to calculate average value to get center of all joints. And then normalize the original coordinates. How can I calculate ...
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0answers
11 views

Calculate weighted mean based on simple mean

I need to calculate the mobile weighted mean of a quantity, $a_i$, based on $b_i$. I have a tool that allows me to calculate the mobile mean of a given series, so we can say I have a function: $F(...
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0answers
18 views

Logarithm in terms of a “biased” harmonic geometric mean

As it was proved in this answer, "the harmonic geometric sequences don't lead to a new concept and behaves as reciprocal of arithmetic geometric sequences". However, consider this "biased" HGM ...
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0answers
30 views

how to answer “A person makes x visits on average”

I have data in the below format How would you calculate average visits per person? Is it: A. (total visits)/(total people) -> 3.33 Or B. Average(visit number) -> 2.4
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0answers
20 views

Calculating the Mean of a Range with Floor and Ceiling Functions?

I did a survey a couple months back, and one of the questions required a range of numbers. I may have discovered my own formula for how to calculate the mean of a range of numbers, but I don't know ...
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1answer
12 views

Averaging scalar fields across an interface

I have a 1D,2D,3D (line/square/cube) of unit dimension which is separated by an flat interface into two regions. A scalar quantity(p) with a jump discontiuity is defined in this domain. I know the ...
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0answers
11 views

Non linear matrix system with average values

I am currently working on a system for the evolution of a vector $X=(x_1(r),\cdots,x_N(r))$ as a function of the variable $\displaystyle{t}$. I have: For $j=1$: $\dfrac{\mathrm{d}x_1(r)}{\mathrm{d}t}=...
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0answers
23 views

Can You Derive Weights Given a Weighted Average?

I wonder if it is possible to derive the weights for a weighted average if the formula is known. For example, let's say we have the following formula Overall Score (10pt scale) = (Weighted Avg. of ...
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2answers
69 views

Average value relating to probability

What is the average value relating to when a value different from a specific six-sided die is obtained?
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3answers
63 views

Average value that seems hard to calculate

What is the average value John obtains when he rolls standard six-sided die and he rolls again when he obtains a certain value?
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1answer
40 views

Which is the correct way to determine the mean result of 1d12 reroll 1s & 2s?

I know the mean is simply the sum of the members divided by the number of them, so the average value given by rolling one $12$ sided die once is $(1+2+3...11+12)/12$ for $6.5$. Straightforward enough. ...
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0answers
11 views

Expected number of neighbors in an Area with Random Uniform distribution

In an area of ${100m^2}$ 19 sensor nodes are uniformly and randomly distributed. Root node is located at the center of this area. Each node has a transmission range of 40 meters in all directions. All ...
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2answers
52 views

Linear functions versus Logarithmic and Exponential functions

If a function is linear, I know that this should be true: $$ {f(x_2)-f(x_1)}={f(\bar x)} $$ Where $\bar x$ is the point exactly in between $x_1$ and $x_2$. Now, I know from looking at their graphs ...
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0answers
49 views

What is the best way to calculate the “percentage difference” between 2 numbers?

In physics and economics courses, we often calculate the "percentage difference" or "relative change" of two numbers. Different teachers instruct students to do it in different ways. If we want to ...
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0answers
24 views

Predict traffic over a node for the next day given traffic on current day

Suppose I am observing the traffic over a network node every minute of a single day. At the end of the day, I have a table of observations like this: ...
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1answer
37 views

How to calculate weighted average with a zero?

I've got zero that needs to be weighted at 40% I've then got a whole bunch of numbers let's say the average of 3,2,1,1,1 all weighted at 40% I've then got another set of numbers, let's say the ...
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0answers
18 views

Linking two dependent equations in a moving average

I have a time discrete system where I need to perform an average of values in a total time n. However, the values are separated with different windows. The process follows like below: After each ...
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0answers
31 views

Proving a statement about the average value of a function

I'm working on a rather complicated problem. And in that problem I (for assumed) that the transient or start-up phenomenon does not influence the average value of a function. My question is, can I ...
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11answers
3k views

Why is the inverse of an average of numbers not the same as the average of the inverse of those same numbers?

I have a set of numbers (in my case: mean retention time (MRT) in the stomach (h)) of which I want to calculate the average gastric passage rate (/h). Gastric passage rate = 1/MRT. My question is why ...
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1answer
26 views

Limit of an arithmetic average series

Sorry in advance as English is not my primary language. I randomly thought of the following simple problem, and I coudn't solve it after one one hour trying. Maybe you guys can help. Let $a_1$ and $...
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0answers
16 views

Sliding weight equation used for temperature averaging

I've looked for previous related questions with no luck, so I apologize if this has already been answered. I may not be phrasing it correctly! I am trying to determine a weighted average that is ...
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3answers
35 views

Calculate the winning probability when using two dice with a different number of sides

I have two players with one die. The first player throws a die between 1 and 125. The second player throws a die between 1 and 350. The winner is the person who gets the higher roll. How do I ...
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0answers
15 views

Random walk with accumulation of penalties

Let a random walf with a certain stopping time $T$. Say that step $i$ costs $i$. If we can compute the average value of $T$, what is the correct (non biaised) way to compute the average cost? Le $E(...
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2answers
437 views

Find a number having minimum sum of distances between a set of numbers

Lets say we have a set of numbers $\{ 5, 7, 1, 2, 5, 100 \}$. I want to find a number $x$ such that the sum of distances of every number from the set to $x$ is minimal. My first thought was that $x$ ...
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1answer
30 views

Average calculation

I know it will be a stupid question for somebody but I need to understand. Below the matrix: $$ \left[ \begin{array}{cc|c} 55&0&0\\ 55&0&0\\ 15&8&53\\ 15&4&27\...
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1answer
12 views

Calculate average/probability of an action happening in a shrinking pool

I'm not sure how to title this actually, so I'll try to explain it better. Let's say I have a bag of 50 items. In there is one particular item that I want. Obviously, the probably of getting that ...
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2answers
62 views

Prove the following logarithm inequality.

If $x, y \in (0, 1)$ and $x+y=1$, prove that $x\log(x)+y\log(y) \geq \frac {\log(x)+\log(y)} {2}$. I transformed the LHS to $\log(x^xy^y)$ and the RHS to $\log(\sqrt{xy})$, from where we get that $...
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1answer
123 views

Darboux continuity of the function $f(x) = \limsup_{n \to \infty} \frac{(x_{1}+…+x_{n})^{2}}{n^{2}}$

Let $f : [0,1] \to [0,1]$ be a function that assigns to each $x \in [0,1]$ the following value: $$ x = 0.x_{1}x_{2}x_{3} \ \ ... \hspace{0.3cm} \text{be the binary expansion of }x $$ define $$ f(x): ...
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0answers
27 views

Best Average to Represent Quantitative Data?

For a final assignment, my two group members and I have created a biased survey called Should Public Schools Implement a Uniform Policy? We have about 2-3 ...
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1answer
27 views

significant figures in averaging samples

I can't seem to find anything about this but I thought that for every 10 samples (of the same thing) that you averaged together you gained 1 significant figure. You'd maybe need 100 samples to gain 2 ...
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4answers
256 views

If $f(x)=\int_{x-1}^x f(s)ds$, is $f$ constant? Periodic?

I was thinking of periodic functions, and in particular the following type of condition: If a function $f:\mathbb{R}\to\mathbb{R}$ always "tends to its average", then it should be periodic. To ...
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0answers
34 views

Calculate average wind velocity

I've got an anemometer to measure wind speed. Its ratio is $50Hz = 15.5m/s$, so my Arduino counts pulses in 3100ms, which should give a count of $100 = 10m/s$. I can display this on a dashboard on ...