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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64 views

Estimating $\sum_{k=1}^N a_kb_k$ given the means $\bar a_k,\bar b_k$ and determining the error

I need to calculate the following expression: $$\sum_{k=1}^N a_k b_k$$ I know the average values of $a_k$ , defined as $\overline {a_k} = {\sum_{k=1}^N a_k \over N } $ and $b_k$ , defined as ...
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563 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
39 views

For N-day moving average, how is N parameter called?

I'm looking for a good name for the variable. Average window length? Sounds like a term for a glass cutter.
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1answer
802 views

Weighted Average of Percentage Increases

I believe I have quite a simple problem, but want clarification on whether it is the best method to use. Say I have have insurance line, and the net income (£) from this business for 2011, 2012, 2013 ...
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1answer
58 views

How to figure out that 95 pecentile of time calls came back within certain milliseconds

I am working on a project in which I am supposed to do profiling on our REST Service. And after that figure it out how much is the ...
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1answer
535 views

Expected value of a multivariate distribution

Given this random vector: $$ \mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} $$ And this probability distribution function that takes it as argument: $$ f_\mathbf{X}(\mathbf{x}) = ...
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2answers
128 views

Calculating new vector positions

I'm using the following formula to calculate the new vector positions for each point selected, I loop through each point selected and get the $(X_i,Y_i,Z_i)$ values, I also get the center values of ...
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1answer
278 views

Calculate vector position

I'm trying to calculate & move vertices to their average "radius" and form a circle from these new positions. Example: I have 8 vertices selected, I have a little script in Maya that will iterate ...
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1answer
374 views

Intuition calculating average price change

Given two products p1 and p2, each with a price per single unit and an amount per year. The question is to calculate the average change in price for both products combined. ...
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1answer
68 views

Calculating expected value

Here is the problem. In a game(shown below) with the marker in the center on each turn the marker moves to a neighbouring region with all positions equally likely and the player collects the cash ...
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2answers
1k views

How can I find the average y value of a function on a given domain?

Lets say that $f(x) = (10 - x)\ln x$. Over the domain: $1 ≤ x ≤ 10$. How can I find the average value of $y$ over this domain and what is that value?
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1answer
115 views

Derivative of a 'weighted average' of decreasing fractions

I'm having some trouble showing the following statement (which intuitively seems to hold): Suppose I have a series of fractions indexed by $i$ , each of them a function of $N:f_{i}\left( N\right) ...
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1answer
275 views

Minimum Numbers to find the given average.

Average score of the player (sum of scores in all the games / no. of games) is given. How Can we find the minimum number of games the player should have played to achieve that average. scores are non ...
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3answers
2k views

How do I find the average of a section of a curve?

I've done some research already and discovered that the formula I need to do this is $$\frac{1}{b-a}\int_a^b f(x)\;dx$$ With $a$ and $b$ being the start and end points of the section of curve I want ...
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2answers
103 views

Maximum Profit at which combination

A dealer deals only in colour TVs and VCRs . He wants to spend up to Rs.12 lakhs to buy 100 pieces. He can purchase colour TV at Rs. 10,000 and a VCR at Rs. 15,000. He can sell a colour TV at Rs. ...
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1answer
307 views

Error Metric which incorporates both mean & standard deviation of data in euclidean space

For simplicities sake (the actually problem is more complex)...Let say I have a set of n 3d points, whose position move over time. For all pairs, I have calculated the mean and standard deviation of ...
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1answer
159 views

Determining the error from a list of individual errors

I have a list of values each with a corresponding error. I can determine the average/mean of the list, but I'm not sure how to best calculate the error over the entire population. e.g. ...
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1answer
113 views

changing values ​​in a distribution without changing the average

I have a set of positive values and I need to increase or decrease this set by adding or reducing number of values. But I would like the mean of values is not altered much. Example: I have this array ...
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1answer
250 views

math distribution of averages and distribution of standard deviation for comparison of bytes

Let me change my question: I have a sequence of 512 numbers (these 512 numbers can have a value between 0 and 255) (in computer mode these numbers can be between 00000000 and 11111111 (bits)). For ...
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1answer
13 views

Adding up numbers * weights to get a result (not weighted average), does it have a meaning?

I have been comparing two solutions and used weights for individual areas based on their importance. I was interested which solution is better, i.e. which one has the higher score. The thing is I ...
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1answer
30 views

How to set up this algorithm?

I'm doing a simple budget app, to make some calculations to improve private economy. I've made an option where you can enter the value of the money that are in the bank right now, and how many days ...
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0answers
25 views

Comparing two populations

I have sampled from two separate populations, and I want to figure out which population is better. Population 1 has an average score of 84.1 and a standard deviation of 11.8. Population 2 has an ...
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2answers
22 views

Is that possible to get all possible numbers, if I have only an average value, max, min number & also number of numbers?

I tried to find out the all numbers or set of possible combination of numbers. But I have only the averages value, maximum number, minimum number & also have tolal number of numbers. ...
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1answer
22 views

Averaging data with different weights, and interpreting the results

I am trying to understand how to average certain data, interpret the result of that, and potentially convert the results to percentages. I have four categories for the data: 1: (0-50%): Not Well ...
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0answers
17 views

Calculating a moving average where the weight depends on the new value

I am attempting to write a small piece of code that tracks the both the time taken to render a frame in a single instance, and a more smoothed value that remains stagnant enough that it can be read by ...
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0answers
29 views

Math Average Basics, Error % calculation, and Blood Pressure.

I saw on the Olympics once when they were doing scoring for team events, that on some events the judges would take each members performance, eliminate the highest and lowest members performances, and ...
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1answer
14 views

Better Rating Result instead of Average

In my database, each item has a total_votes and total_ranking. When a user vote, I add +1 to the total votes and add its rating ...
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1answer
72 views

Maximum and minimum average question

During a cricket match, India playing against NZ scored in the following manner: Partnership | Runs scored 1st wicket | 112 2nd wicket | 58 3rd wicket | 72 4th wicket | 92 5th wicket | 46 6th ...
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1answer
55 views

problem in understanding overall change in average

The average weight of 5 men is decreased by 3kg when one of them weighing 150kg is replaced by another person. This new person is again replaced by another person whose weight is 30 kg lower than the ...
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2answers
39 views

Estimated wait time for a library book

A library has 20 copies of a book that circulates for 3 weeks. All copies are out and there 40 people on reserve ahead of me. How do I estimate the wait time?
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1answer
16 views

Simplifying an indefinite integral representing the calculation of an average

I have an equation for a term $z_i$: $$ z_i = \ln\frac{a_iR+p_i}{T_o* tan\theta_i } $$ This represents a value in a grid, at location $i$, with the grid representing a geographic area. To get the ...
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3answers
130 views

Probability of two normal random variables when random samples are taken from a population

This is sort of second section to my previous question, I should have included both together, but I forgot to. Sorry for any inconvenience. X= random height of a male Y= random height of a female X ...
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1answer
46 views

Meaningful statistic measure of data pairs

I have a dilemma. I have pairwise data, (a,b), that represents some form of speed, whether it's miles/hour or megabits/second. Let's say that we have the following set of data from measuring the ...
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133 views

About Bayesian formula and rating system

I'm building a scoring system with score from 0 to 5) and I would like to sort products according to the number of reviews and their scores. After some research on the Internet I have found two ...
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2answers
37 views

For any base-$n$ number system, what is the average length of a number $\leq100$?

By this I mean the amount of symbols (bits / digits / etc. ) for any number from $0$ to $100$. I don't know whether this can be answered, I'm just asking out of interest - not homework or anything.
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1answer
17 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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1answer
178 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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0answers
34 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 ...
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2answers
79 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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0answers
55 views

Finding possible numbers to yield a certain arithmetic mean (average)

I'd like to know how I could find the possible numbers to yield a certain average number (arithmetic mean), given that: the arithmetic mean will be calculated from 20 integer numbers, each having a ...
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2answers
161 views

Average number of people required to find a pair with same birthday

I have to find the expected number of people required to find a pair with same birthday. This is what I tried: Assume that there are $M$ possible birthdays, then following the definition for expected ...
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0answers
90 views

Deal or No Deal: Arithmetic, Median or Geomtric mean?

I'm trying to decide which type of mean is best to use when playing Deal or No Deal (in terms of comparing it with the Banker's offer). I realise the standard answer would be the arithmetic mean, but ...
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0answers
24 views

Estimator of Absolute Error?

Given $X \sim B(n, p)$, we know that $\hat{p} = X / n$ is the obvious estimator for unknown parameter $p$, and the following quantity $$\frac{\hat{p}(1-\hat{p})}{n-1}$$ has the property that its ...
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1answer
47 views

Difference between $\sum_{i=1}^{k}{\frac{s_i}{kn_i}}$ and $\frac{\sum_{i=1}^{k}{s_i}}{\sum_{i=1}^{k}{n_i}}$

I am getting confused at how to calculate the average probability. Suppose we repeat a kind of binary survey $k$ times each of which was done on a completely separate sample group. For each $i^{th}$ ...
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545 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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0answers
34 views

Is $x_1^{\alpha_1} + \dotsb + x_n^{\alpha_n}\geq x_1^{h/n}\dotsb x_n^{h/n}$ an example of power means?

I learned here that there is a relation between weighted means of the form $x_1^{\lambda_1}\dotsb x_n^{\lambda_n}$ and $(\lambda_1 x_1^r + \dotsb + \lambda_nx_n^r)^{1/r}$, namely that the former is ...
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63 views

Difference between $\frac{1}{n} \sum_{i=0}^n \frac{b_i}{a_i+b_i}$ and $\frac{\sum_{i=0}^n b_i}{\sum_{i=0}^n a_i + b_i}$

Consider scenario like this: each user can add movies. each user can rate movies he added. I want to know how many movies average user has unrated (as in average percentage). Let's translate this ...
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2answers
1k views

How to calculate weight of positive and negative values.

We have used formula formula to calculate weight as, $$ w_1 = \frac{s_1}{s_1 + s_2 + s_3};$$ $$ w_2 = \frac{s_2}{s_1 + s_2 + s_3};$$ $$ w_3 = \frac{s_3}{s_1 + s_2 + s_3};$$ However, their is ...
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0answers
66 views

How to measure the time-decayed rate of independent event

I have events arriving in a software system at a variable rate. Imagine these events are, say, hits on a website. I'd like to periodically report on the rate of arrival of events over a number of ...
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1answer
200 views

weighted average

I'm not sure the correct term for my problem is weighted average. But let me explain. I've conducted a survey where participants answer on a scale betweeen $1$ and $7$. The questions fall into three ...