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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Calculating a new average without having the full set of no.s [duplicate]

Say we have the below data: 100 120 80 110 The average of these is 84.5 Is there any way, I can store some data from this original data and calculate new average ...
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Recalculate average based on subset of poisson distribution

Assuming a series of independent events, probability of the event occurring on a given day is a poisson distribution with λ=0.8. This includes probability of event ...
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Decision to use median or average in a skewed or uniform distribution [closed]

Goal: To determine whether to use the median or average (or a weighted combination of the ...
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Terminology question over means and probabilities

I have two variables. The first is a straightforward mean taken over the limited space $s\in\Gamma$ rather than $s\in\infty$. Whereas the second is that same variable divided by the probability of $\...
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Calculating the weighted average with a minimum

I'm looking for a way to calculate the weighted average of a range of numbers, but where the lowest need to be 5% (and thus the total still needs to be 100%). Let me try to explain: ...
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Skewed data: choosing the average or median

Goal: The data below shows (in order) the date, median, average, ...
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Is it True: The average distance of points from the diagonals is less than the average distance from circumference of the circle in a rectangular area

My problem is related to proving that the average distance of random distributed points from the diagonals is less than the average distance from the circumference of the circle. The problem is ...
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Calculate Sarah's Minimum Score

Question: In order to graduate, Sarah has to make an average score of at least 90. If he made 95 and 94 on his first two tests. What should his minimum score be on her final test in order to graduate?
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How many students with scores below 60 points at most?

There are 30 students in the class. In a test with a full score of 100, the average score of the class is 90 points. How many students with scores below 60 points at most? A. 8 B. 7 C. 6 D. 5 E. 4 My ...
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Averaging estimates of probability

Say one weather forecaster says there is an 80 percent chance of precipitation at a given place and time. Another forecaster says there is a 30 percent chance. I have no reason to think one forecaster ...
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I am trying to calculate the change of Geometric mean, but they don't match

I have Day 1 data and Year 1 Data, and I used R to separately calculate their geometric mean as Gmean(low$day1) and ...
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How to solve the average?

Question: "The average marks of the students in four sections A,B,C and D together is 60 %. The average marks of the students of A,B,C and D individually are 45%,50%,72% and 80% respectively. If ...
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How do I calculate for the change in value?

Question: "In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age , so the ...
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why is average of a random subset the same of the initial set

This feels like a really simple question, plus it looks very intuitive, but I can't find a formal proof or anything that proves it. I have an initial set X with n values. I extract Y, a random subset ...
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Giving weights to multiple choice question with multiple groups

So my problem is the following: I have made a survey composed of only one multiple choice question. This question has 5 possible answers. For simplicity, lets say the answers are Blue, Green, Red, ...
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6 votes
1 answer
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Inequality help: $\frac{a+b+c}{3}\geq\sqrt{\frac{ab+bc+ca}{3}}\geq\sqrt[3]{abc}$

I'm working through "Calculus of One Variable" by Joseph Kitchen, and this inequality (problem 3 from section 1.3) is causing me quite a bit of pain to prove: $$\frac{a+b+c}{3}\geq\sqrt{\...
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Is it possible to calculate the total average between two sets of numbers, without just using the sum of each set of numbers?

I'm working with some really frustrating reporting software that doesn't let me calculate the average by dividing two sums. To get around this, I need to find a way to get the same result by ...
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How to find the average "direction" of a set of vectors?

There are a lot of similar sounding questions I have found but none match my problem. I have a set of 3d vectors (x, y, z) that represent acceleration in 3 axis, the values come from a real life ...
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Determine my increments from average

I am trying to find my cost increments in a situation where I know my average cost for 5 situations, but don’t know the values of each situation. My cost is 300 average for past year per tests/...
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How to prove this inequality involving two weighted averages?

Let $f$, $g$, and $h$ be continuous real functions with strictly positive values. $f$ is strictly increasing. $M, N>0$ are constants, and $a\in(0,1)$. Can you prove (or disprove) the following ...
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2 votes
1 answer
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Why arithmetic mean gives the closest number in a data set? [duplicate]

I just enrolled in AP Statistics course this week. And, one thing that popped up a lot in descriptive statistics is the idea of the mean. I understand mean as the closest data point to all of the data ...
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2 votes
1 answer
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What are the geometric, harmonic, and quadratic averages of a function?

In Mean of a function, they describe the arithmetic mean of a function and at the bottom of the article they said: There is also a harmonic average of functions and a quadratic average (or root mean ...
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Moment inequality for average of centered iid random variables

Let $X_1,X_2,\ldots,X_N$ be a sequence of i.i.d. random variables such that $\mathbb{E}[X_1]=0$ and such that $|X_1| \leq m < \infty$ almost surely, and let $$ \bar X_N = \frac1N\sum_{i=1}^N X_i $$ ...
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Calculate users overall percentage for daily quiz

I have a daily quiz where a user has 3 attempts to answer correctly. So they will either answer on attempt1, attempt2, attempt3 or be wrong. I store the daily answer rate for each individual date and ...
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Average wind direction and speed computation

I am trying to compute the average wind direction and speed based on several data of direction and speed given by my weather station. I am following this algorithm, however, I don't understand what ...
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Finding integral average form 0 to infinity of a step function

I'm supposed to add a perturbation to $$f_0(v, x, t)= \begin{cases}p(x, t), & v<u(x, t) \\ 0, & v>u(x, t)\end{cases}$$ Getting $ f(x,t,v) = A(x,t) + g(x,t,v)$, where the isotropic part $...
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Term for the mean of the minimum and maximum of a set of real numbers

I've been programming something for a few days now, and there's a concept I find myself lacking a name for that I feel like I should know offhand. Is there a term (generally accepted or otherwise) for ...
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4 votes
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How do we naturally extend the average from the Hausdorff Measure for functions with a domain without a gauge function?

Motivation: According to this question Some sets have a Hausdorff Dimension $\alpha$ but have a zero-dimensional Hausdorff Measure. These sets may have another dimension function, i.e. a function $h:[...
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1 vote
1 answer
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"Average" of Cartesian coordinate systems

Having two Cartesian coordinate systems: C1(X1,Y1,Z1) C2(X2,Y2,Z2) (where X1,Y1,Z1 and X2,Y2,Z2 are orthogonal unit vectors) Is it possible to have a third ...
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1 vote
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Help calculating the expectation of the square of the average of random variables

I have $\bar{X_n} = \frac{1}{n}\sum_{i=1}^n X_i$, where the $X_i$ are iid Bernoulli with parameter $p$, and I want to find $\mathbb{E}[\bar{X_n}^2]$. When I do this by deriving it from the variance, I ...
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How to define the average of a multivariable function in infinite space?

We know that the average of a function $f(x)$ where $f: \mathbb{R} \rightarrow \mathbb{R}$ in the interval $[a,b]$ can be computed by $$ \langle f(x) \rangle =\frac{1}{b-a}\int_a^b f(x)dx. $$ How ...
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Average time to roll 1 on a die whose faces increase with each roll.

Context: Although I am comfortable with much of undergraduate-level math, probability is something I rarely venture into, bizarrely. Hence, I thought I'd come up with a recreational problem. Suppose I ...
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1 vote
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A (finite) average can be calculated by averaging all the possible selections of order k [closed]

I want to formaize something that looks quite trivial. Let X be a set of numbers. Let $\bar{X}$ be an average of a set X. And let ${X_k}$ be the set of all sets with a size of k exactly. And let ${\...
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Why on average, is $A[j]$ smaller than half of the elements of $A[1\dots j]$

This is a phrase from the book "Introduction to Algorithms" 3rd edition page 28. Suppose that we randomly choose $n$ numbers and apply insertion sort. How long does it take to determine ...
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Which step is logically incorrect in this obviously wrong manipulation? [closed]

Consider $2\times3$. The above multiplication is just $2\times3=2+2+2$ or more generally $a\times n= \underbrace{a+a+.....}_{n -times}$ Now consider $$\bigg \langle\frac{1}{r^2}\bigg\rangle=\bigg \...
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4 votes
2 answers
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How to keep numbers within an average without them being all the same

Background: I am developing an app to make calculations for worldbuiding, following the instructions given by the YouTube channel Artifexian. In one of the videos, he mentions a formula to keep the ...
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7 votes
1 answer
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How many $01$ or $10$ substrings are there, on average, in a random $n$-bit string containing $k$ ones.

For example, if $n = 4$ and $k = 2$, then we have ${4 \choose 2} = 6$ strings: $$ 1100 \rightarrow 1\\ 0011 \rightarrow 1\\ 1001 \rightarrow 2\\ 0110 \rightarrow 2\\ 1010 \rightarrow 3\\ 0101 \...
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Percentage of contribution using average

I want to calculate how much an individual employee in a Business Unit (BU) of a company contributed to the overall total expense (salary) of that BU. I have the company wide calculated Average Salary ...
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3 votes
1 answer
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Where is the missing ratio?

On a day at the Fruits Exchange, an apple can be exchanged for 2 bananas, and a banana exchanged for 2 oranges. The market is perfectly efficient, so an apple can be traded for 4 oranges. On another ...
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Are the power mean inequalities still valid when they are generalized to continuous functions?

I need to measure a mean value of a function $f(\mathbf{x})\geq0$ defined over a domain $\Omega$. It would be very useful to me to be able to parametrize this mean value so that: $$M_{-\infty}(f)=\min\...
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Find analytically the statistical average $\langle f\rangle$ of function $f(x)$ when sampling x a large number of times.

I have a function $f_n(x) = \frac{1}{3} + 2x \left( \frac{1}{3x} \right)^n$ Where n is a natural number larger or equal than 3 and a constant. I am sampling the value of x numerically in the interval ...
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Summation about an inverse-variance weighting average expression with a unique random variable considered

The context is about astrophysics but this is actually a mathematical issue. We want to define a physical observable which allows to derive some estimations of errors on parameters fiducial values. ...
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Estimating Right Censored Values

I'm a newbie at Math, and I am just getting my feet wet when it comes to understanding math and statistics so please forgive my ignorance or question if it's already been answered or if materials are ...
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How do I interpret weighted and non-weighted gains on a stock portfolio?

I have the following stock gains and losses for a stock portfolio. Overall, the portfolio has lost $40 or 28%. But when I calculate weights based on market value, and then calculate the gain/loss ...
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1 vote
1 answer
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If two points are chosen at random from the Cantor set, what is the average distance between them?

I've so far figured that I need to look at different cases for if the points are within the lower or upper third of the Cantor set, but am confused on how to proceed beyond that to take an average for ...
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Finding a formula to calculate the final grade acquired.

the question is as follows. Assume a student has got 4 assignments that will determine their final grade. Note, the grade ranges from 6-10. Assignment 'A' accounts for 15% of their final grade, 'B' ...
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6 votes
1 answer
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Computing an Exponential Moving Average Via Convolution

According to the Wikipedia page on moving averages, "This is also why sometimes an EMA is referred to as an $N$-day EMA. Despite the name suggesting there are $N$ periods, the terminology only ...
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Lag of a delagged exponential moving average

An exponential moving average $EMA(Y_t, N) = S_t = \alpha Y_t + (1 - \alpha )S_{t+1}$ applied on a time series $Y$ with a finite and moving calculation window of $N$ lags $\frac{N - 1}{2}$ on average. ...
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Is the limit of the mean value of a function around a point equal to the value of the function at that point? [closed]

Suppose that the function $f:\mathbb{R} \rightarrow \mathbb{R}$ is continuous. Is the following statement correct? $$\lim_{n \rightarrow \infty}\frac{n}{2} \int_{y-\frac{1}{n}}^{y+\frac{1}{n}}f(x) \...
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Handling of infinite utility children when backward inducting into a Nature node of a Expectiminimax game tree

Background I am coding a game playing engine for a (3+, but for now assume) 2 player card game, which has a shuffled (AKA random) & face down (AKA hidden) deck. This game has perfect* and complete ...
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