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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13 views

Finding average time to run a marathon

Here is a problem that I am working on. I have tried to put it in simplified and analogical terms here and it may sound a bit absurd but I am desperate for a solution. 100 runners start a 5 day ...
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2answers
38 views

Computing the average difference in a list of numbers

I have a list of numbers 280, 449, 689, 959, 1360, 1740, 1139 so there is between 289 and 449 is a distance of 169 and then between 449 and 689 a distance ...
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1answer
16 views

Features of a Set Given Same Value for Maximum and Average

What else, if anything, can be said if the maximum of a set is equal to the average value in the set? If the average is equal to both the maximum and minimum then all the values are the same, but can ...
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21 views

Economics Marginal Cost and Average Cost

I am in Computer Engineering but this year the university gave me choice for two electives with one being Psychology and the other Economics...So this being my first economics course I am really ...
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1answer
29 views

How to normalize a slope?

Say I have two slopes and two averages for a sample: $m=4{,}000$ dollars/day, average $a=50{,}000$ $n=80{,}000$ dollars/day, average $b=700{,}000$ Graphically, $n$ is very ‘steep’ compared to $m$. ...
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1answer
31 views

Is the norm of the average $\le$ the norm of the max?

Given $\pmb X \in \mathcal{R}^p$, denote the elements of $\pmb X$ as $\pmb x_i$ for $i= 1, \dots, n$. Denote the $t(\pmb X)$ as the average of $\pmb X$ \begin{equation} \pmb t(\pmb X) = \frac 1 n ...
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1answer
22 views

fast solve average

there are Indians and Europeans in an army of 12,000. the average height of Europeans is5'10" and that of Indians is 5'9" and the average height of entire army is 5'9,3/4. find out the number of ...
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3answers
33 views

Covariance Issue with a joint distribution

Here is the problem: Let $X$ and $Y$ be continuous random variables with joint density function: $$f(x,y) = \frac{8}{3}xy\text{ for }0 \le x \le 1\text{ and }x \le y \le 2x $$ I'm trying to find ...
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2answers
52 views

How to establish this inequality: $(1-a)(1-b)(1-c) \geq 8abc$ for $a+b+c=1$?

Let $a$, $b$, and $c$ be positive real numbers such that $a+b+c = 1$. Then how to establish the following inequality? $$ (1-a)(1-b)(1-c) \geq 8abc.$$ My effort: Since $a+b+c =1$, we can write $$ ...
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1answer
43 views

What is the most elementary proof of these inequalities?

Let $p$ be a non-zero integer, and let $x_1$, $\ldots$, $x_n$ be $n$ positive real numbers. Then we define the $p$-th power mean $M_p$ of these numbers as $$ M_p \colon= (\frac{x_1^p + \ldots + ...
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2answers
29 views

Proving that mean KDR in a videogame is one

This is not related to schoolwork. A friend of mine challenged me to prove that the mean KDR (assuming players can only die at the hands of other players) must always be equal to one. I have gotten ...
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1answer
27 views

How to find the average value of a discontinuous function

A car covers $\frac{1}{3}$ distance with speed $20\frac{m}{s}$ and $\frac{2}{3}$ with $60\frac{m}{s}$. What is the average speed over the entire interval? Due to the discontinuity of the function, I ...
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2answers
23 views

Comparing / Averaging two very different numbers

I have two examples called a and b. Each example has two scores: a: 0.5 and 0.001 b: 0.8 and 0.0001 If the higher score wins, then b wins when looking at the first set (0.8 > 0.5). But I also want ...
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1answer
23 views

What ratio of students in a 20-student class with total average of 17.06 got at least 17?

The maximum score is at most 20. The class has 20 students. For math exam the average of the whole class is 17.06. How many per cents of the class got at least 17 out of 20 in the exam?
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1answer
23 views

Average sum of seria

I need some help with the next question in probability: In the range {1,2,...,100}, someone picks randomly 15 different numbers, with the same probability for each number. What is the average sum ...
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1answer
16 views

How should I calculate weighted average in this case?

If there is a product, whose price depends on its quality, and these price values are: [0.6; 1.1; 1.3; 2.0; 4.2; 21.6] Lets assume that there is some kind of a lottery, and I can by a ticket for it ...
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1answer
11 views

Working out a parent percentage from child percentage

I am currently working on a performance indicator system for the number of reviews due on a bunch of document against the number that were due in that month as a percentage. There are several areas ...
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2answers
34 views

average and total average

why is it when I get the average of the column "per hour", it's different from the total?
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8answers
3k views

Unorthodox way of getting the average of two numbers

I can't believe the alternative method I just saw to calculate the average of two numbers: ...
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3answers
39 views

Help with question about Normal distribution

The heights of people at some city is $N(\mu,\sigma^2)$. 25% of the people are above 176 cm. and 20% are below 165 cm. How do I found $\mu,\sigma^2$? We choose randomly a group of 100 people. What ...
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0answers
22 views

Mean values using eigenvalues - how?

I thought the definition of the average value of $f(x)$ was $f* = \frac{1}{T}\int_0^T f(t)dt$ How do I get from this definition to the definition of the mean value of a function in terms of ...
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1answer
18 views

Approximate simple moving average knowing only previous SMA?

I know it's possible to calculate a regular average incrementally knowing the previous average, the next number and the number of items. But is this possible for a moving average of N items, at least ...
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2answers
43 views

Calculating average value of points over a period of time

I have several values plotted over a period of time on a line graph. The length of time between values is not uniform (i.e. one value could be 3 days after the one before, which itself could be 2 ...
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1answer
37 views

Average value calculation

A company has 2 mines: A and B. The production per person in mine A was 22,6 tons last year, and 27,9 tons in mine B. Last year 60% of the total production came from mine A. The question is the total ...
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1answer
23 views

Problem about average of cos square (nt) where n is arbitrary

I often see people just say time average of cos^2(nwt) is 1/2, I want to know in what cases this is not valid? w is just the frequency, can be assumed as a constant. Assuming you are always ...
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1answer
27 views

Mean squared [X] or Mean [X] squared?

If I have two functions, as below, which one is "Mean [X] squared" and which is "Mean squared [X]"? Would I be correct in saying the former is number 1 and the latter is number 2? Thanks in advance ...
3
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1answer
16 views

Choosing two sets of values with the least difference between the averages of the sets

This is probably a simple Combination problem but I can't think of how to solve it in LibreOffice. I run multiplayer games along with seven of my friends, on two teams of 4 players each, for a total ...
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1answer
24 views

Does missing a number from a set affect the average?

Firstly, apologies for an uninteresting title, and whether this is absolutely newbie maths. I'm a programmer, and when it comes to maths and me - the wheel is going, but the hamster is dead. On To ...
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1answer
45 views

Average distance from center to random point in rectangle

I need to find average squared distance from center in rectangle. One edge is 2, other one is 1. On my understanding I need to find $$E[X^2+Y^2]$$ So I got ...
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0answers
18 views

Volume of a Part of a Triangular Prism Enclosed in a Sphere

I'm having trouble finding the volume of the shaded prism. I know how to calculate the volume by extending the height of this prism to create a triangular based pyramid, but I cannot get the same ...
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1answer
101 views

Calculating Average Time based on Success Probability

Interns of company XYZ has to pass 2 training programs in sequence. So Program 2 can only be taken after an intern has done Program 1. Each program has a success rate of 40% and each program takes 3 ...
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9 views

Average unused capacity of three capacity units

Let's say that there are 3 capacity units that have the following maximal capacities: ...
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1answer
18 views

How to calculate new mean if population is unknown?

I have three values Mean (population mean, not from sample) $\bar{x} = 3$ Number of elements in population (number of values in original set) $n = 15$ A new value $x_{(n+1)} = 7$ What is ...
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1answer
20 views

Likelihood across multiple averages… Sorta

Hopefully my title isn't misleading... i'm not sure what this math problem is called, making searching for the answer quite difficult. Maybe someone can tag this question appropriately if you know the ...
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2answers
17 views

Is there a formula for finding the series of numbers based on an average.

So I am working on a program that does a scrolling effect. the image is 1200pixels wide, and each time it scrolls, it should move an average of 2.67 pixels. However I am using a function that does not ...
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1answer
13 views

Calculate a Ranking Average

I got stuck to find a fair formula to calculate the average ranking of the itens that I found after consecutive searches, look: If I calculate the simple average of the item2 for example I get 1,33 ...
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0answers
24 views

Average minimum distance

Let $\mathbf{u} =\begin{bmatrix}u_1 & u_2 & \dots & u_N \end{bmatrix}^T$ and $\mathbf{v} = \begin{bmatrix} v_1 & v_2 & \dots & v_N\end{bmatrix}^T$. All the elements of ...
3
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2answers
117 views

How to find the average value of $y = e^x$ between $x = e$ and $x = 2e$? [closed]

What approach would be ideal in finding the average value of $y = e^x$ between $x = e$ and $x = 2e$?
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2answers
30 views

Calculating mean (Average) of vector

I'm trying to calculate PCA (Principle component analysis) and part of the equation is to calculate the mean of a vector $v$ and subtract each element of $v$ by it's mean. However, is this in column ...
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1answer
14 views

Which average to use with range

Say I wanted to calculate how much rain in terms of volume falls on the Earth each day or hour, etc. In order to do so I'd first need to know how much water is in a single raindrop. I know that and it ...
2
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1answer
52 views

Zonal averaging of partial derivatives

Given a quantity $Q(x,y,t)$, the zonal average operator $[Q] = \frac{1}{2\pi}\int_0^{2\pi} Q\:\mathrm{d} \lambda$, and zonal anomaly $Q^\star$ such that $Q = [Q] + Q^\star$, my text book says that ...
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0answers
26 views

Find spikes in data

I have some datasets and I need to find spikes in them. Imagine the data looks like trading data. If the spike is big enough, I need to log it, otherwise, proceed in the analysis. I tried with a ...
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1answer
44 views

Calculating the average of multiples and divisions

Imagine a number line that contains every value that is greater then (but not inclusive of) 0. The center of the line is 1. On the right side of the center(1), obviously, are all the whole and ...
0
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1answer
18 views

What statistical equation am I looking for?

Suppose you have two data sets: Dataset A: 4,2,6,5,3,3,5,4,4 Dataset B: 8,0,0,8,9,1,1,9,0 Both data sets have a mean of 4, but dataset A's values center much more around the mean whereas dataset ...
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1answer
35 views

Why must average only be used with normal distribution?

In a technical job interview I was asked a question that I couldn't quite make sense of. The interviewer was talking about sampling a sound file to make a visual effect (such as a graph that moved to ...
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1answer
20 views

A Basic Math Question on Averages

Okay this is going to sound really stupid but I'll ask anyway... I need to get a $5.5$ accumulative GPA (the highest is a $7.0$). For the last $16$ classes I've done my GPA is sitting at $5.44$. I'm ...
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1answer
21 views

Running a Cumulative Average

I'd like to run a cumulative average and I'm wondering if my process is sound. Here's a small dataset: Row 1: $\frac{2\cdot 60}{58} = 2.07$ Row 2: $\frac{4\cdot 45}{44} = 4.09$, ...
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0answers
71 views

How to prove the integral function with cosine is increasing

Prove that the following function is an increasing function on $x\in (0,1)$ when $n\ge2$. $f(x) = \int_0^{\pi} \frac{1}{(1-2x\cos\theta+x^2)^n} d\theta$
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1answer
46 views

Fast way to recalculate average and standard deviation as new values arrive

Say I have a stream of values arriving all the time, and I want to get the average and standard deviation of only the last $n$ values. If I already have the average $V$ for values $v_1, ..., v_n$, ...
1
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1answer
35 views

weighted average with exponential weighting

I want to create weighted average, where weights depend on value of number. If I want exponential weights is this regular? $average = \log_e(\frac{\sum_{i=1}^n e^{v_i}}{n})$ Isn't it just average of ...