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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5
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2answers
760 views

How many decimal places are needed for incremental average calculation?

If using the following formula to incrementally calculate average value: $$m_n = m_{n-1} + \frac{a_{n}-m_{n-1}}{n}$$ And the number of decimal places to where you can save $m_n$ is limited to $d$ ...
0
votes
1answer
341 views

Algorithm to Get a Product score based on rating

I am trying to device a algo for product score. Here are the inputs User rates a product on 5 different criteria out of 10 Each criteria has a different weightage with all adding up to 100% There ...
0
votes
1answer
938 views

Calculating Average Percent

I have two ways to calculate the average starting price of an auction item compared to it's actual value. ...
1
vote
0answers
59 views

Taking averages

Suppose I have a function $f(\theta)$ that is a function of the angle $\theta\in [0,2\pi)$. Why is the average of $f$ over a large collection of randomly oriented objects: $$\int f(\theta)\sin ...
1
vote
1answer
337 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 ...
2
votes
2answers
141 views

Calculating statistic for multiple runs

I have s imple, general question regarding calculating statistic for N runs of the same experiment. Suppose I would like to calculate mean of values returned by some Test. Each run of the test ...
1
vote
0answers
39 views

Dynamic Light Scattering

In DLS does the combination of the Time Average and Ensemble Average give a better statistical average than the results shown by each case considered separately ?
2
votes
1answer
142 views

Fréchet mean between points in $\mathbb{R}^3$

Let $X$ be a set of $n$ points in $\mathbb{R}^3$ and $f_m$ be the Fréchet mean, i.e.: $$ f_m= \arg \min_{p \in M} \sum_{i=1}^n w_id^2(p,x_i) $$ where $(\mathbb{R}^3,d)$ is a complete metric space, ...
1
vote
1answer
206 views

How long does it take to complete a sticker album?

We are collecing stickers in chocolate bars and whenever we open a bar we get a random new sticker. There are many different stickers and we try to collect them all. We open the first bar and get a ...
2
votes
0answers
396 views

How can you calculate actual values when all you have is rolling averages?

Let's say you have a set of data that is rolling 6 month averages of the actual monthly data. Good data collection would mean you saved the actual values and then calculated the rolling averages, but ...
1
vote
2answers
56 views

Constructing an average equation - Standardized Test

A question in the standardized test is: The average of $n$ numbers is $a$. If $x$ is subtracted from each number the average will be a) $(ax)/n\quad$ b) $(an)/x\quad$ c) $an-x\quad$ d) ...
0
votes
1answer
54 views

Which of the following cannot possibly be the average - Standardized Test

I came across a question while preparing for a standardized test that is kind of confusing. Hope you guys could help me out here. The question is: Three men have weights that range from 110 to 135 ...
0
votes
1answer
292 views

Calculating average of word problem

I was preparing for a standardized test and came across the following problem: During a closeout sale 30 suits are sold at \$60 each.The price is the reduced to \$50 each and 20 suits are sold. At ...
2
votes
3answers
103 views

Problem with calculating average.

I came across the following question. A man travels a distance of $20$ miles at $60$ miles/hr and then return over the same route at $40$ miles/hr. What is the average rate for the round trip in ...
1
vote
1answer
2k views

Weighted average vs. weighted mean

Is there a formal difference between weighted average and weighted mean? I get corrected to the latter if I type in the former in wikipedia, and then there is a lot of stuff about the name "average" ...
1
vote
1answer
169 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. ...
0
votes
2answers
767 views

Weighted average of two frequencies

This should be really simple but I'm getting stuck and I'm probably extremely dumb.. I know that a machine receives two kind of parts: Type 1 -> with frequency 50 per week, each one is processed for ...
2
votes
1answer
293 views

Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
5
votes
1answer
343 views

Average sine of an angle between two rays in a cone

I'm looking for an average value of sine of an angle between two rays, lying within a cone with a certain angle. Given a cone with an aperture of ${2\chi}$ and two rays lying within the cone. The ...
1
vote
4answers
3k views

Fastest Method to solve this average problem

average of A and B is 71; of B and C is 76; of A and C is 79. How to find the average of A,B,C. I know the way of solving this problem using equations.But it takes time.So wanted to know if any other ...
4
votes
0answers
361 views

Average transformation matrix?

I have several estimates of the transformation matrix between two planes and some values that give some indication of the error involved in the estimate. How can I use this information to gain the ...
2
votes
1answer
375 views

Calculating kWh from multiple watt readings

I have a file which contains watt readings for various times throughout the day. A reading is stored roughly every 6 seconds. ...
2
votes
2answers
2k views

Finding percentile rank without knowledge of distribution

Say you take a test and are told your individual score, as a percentage. Eg: 95%. You are also told the aggregate score (average) of all students together, as well as how many students in total took ...
6
votes
3answers
2k views

Average distance between two points in a circular disk

How can I find an average distance between two points lying inside a circular disk of a certain radius? I wonder if there is any other way except of using a Monte Carlo method?
4
votes
2answers
3k views

Real world examples for Mode in Statistics

I am looking for some real world examples for mode in Statistics involving topics which students like say Football or Social networks. Also they need to clearly identify differences in the usefulness ...
0
votes
1answer
425 views

Error propagation and averages, a practical question

Ok, I'm sure this is simple, yet I'm confused. Lets say my goal is to obtain an average concentration C=N/V so I take a number of N and V readings with errors: $N_1=50\pm2, V_1=100\pm4$ ...
3
votes
2answers
828 views

What do curly brackets mean in this formula?

In this paper, in the Formula at the beginning of 2.2, we have $B=\{b_i(O_t)\}$ where $i=0,1$ - the number of probability formula $O_t$ - the state at moment $t$ $b_i(O_t)$ - two probabilities ...
2
votes
4answers
724 views

Get `n` random values between 2 numbers having average `x`

I want to get n random numbers(e.g n=16)(whole numbers) between 1 to 5(including both) so that average is x. x can be any value between (1, 1.5, 2, 2.5, 3, 3.5, 4, ...
2
votes
1answer
107 views

Is the average of all $x$ such that $0 \le x \le 1$ $ \forall $ $x \in \mathbb{R}$ equal to $\frac{1}{2}$?

Is the average of all $x$ such that $0 \le x \le 1$ $ \forall $ $x \in \mathbb{R}$ equal to $\frac{1}{2}$ ? It may seem this way but how can we show that indeed it is $\frac{1}{2}$. We know that the ...
-1
votes
1answer
2k views

Normalizing a matrix using matrix operations

I need some help in normalizing my matrix. I have a 5X4 matrix A. I want to normalize each column. Following is the explanation on the operations B = Operation of matrix (A) B matrix is 5x4 matrix. ...
-1
votes
1answer
614 views

Calculating a 5 star rating with a reputation number… [duplicate]

Possible Duplicate: 5 star ratings. Bayesian or Weighted average? Similar question, but unlike that question this deals with two factors the stars and reputation. Lets say Stack Exchange ...
2
votes
0answers
244 views

Exponential average of logs

I'm working on a sound recognition algorithm where an "exponential moving average" is used for "adapting" to sound levels. It turns out that taking an average of logs works better than simple sums ...
2
votes
1answer
127 views

What is the best way to average the frequency of Chinese characters in a sentence?

I'm trying to find the best way to assign a "frequency score" to sentences in Chinese. Basically, I have a database which tells me how frequent each Chinese character is. From that, I would like to ...
1
vote
2answers
7k views

Is the average of the averages equal to the average of all the numbers originally averaged?

I am tempted to say yes because of the following pseudo-proof (I say pseudo-proof because I am not convinced): $$ \frac{\frac{w+x}{2}+\frac{y+z}{2}}{2}=\frac{w+x}{4}+\frac{y+z}{4}=\frac{w+x+y+z}{4} ...
1
vote
1answer
49 views

Variant of the modal average

I know that there are variants of the arithmetic mean and the median that are applicable to three dimensional data (centroid and medoid), but have not been able to find such a thing for the modal ...
2
votes
1answer
125 views

How are Tr(AB) results restricted?

In quantum mechanics one postulates that for each state $i$ there is a matrix $A_i$ and for each measureable dynamical variable $j$ (velocity etc.) there is a matrix $B_j$. Both are Hermitian matrices ...
4
votes
1answer
225 views

Prove that if 2000 m is run in 4:50, then one mile is run under 4:00

Prove that if 2000 m is run in 4:50, then one continuous mile is run under 4:00. I was thinking -- yeah, this follows easily from the other question, where I asked that if 2 miles are run in ...
24
votes
11answers
4k views

Prove that if two miles are run in 7:59 then one mile MUST be run under 4:00.

I'm in an argument with someone who claims that a two mile in 7:59 does not imply that one mile (at some point within the two miles) was covered in under 4:00. This is obviously wrong, but I'm not ...
1
vote
1answer
118 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 ...
18
votes
3answers
7k views

Incremental averageing

Is there a way to incrementally calculate (or estimate) the average of a vector (a set of numbers) without knowing their count in advance? For example you have ...
4
votes
1answer
1k views

Regular average calculated accumulatively

is it possible to calculate the regular average of a sequence of numbers when i dont know everything of the sequence, but just everytime i get a new number i know the total count of numbers and the ...
0
votes
1answer
551 views

Weighted mean properties when using angles

Consider a joint angle $j$, such that $-180^{\circ} \lt j \lt 180^{\circ}$, with the true value unknown. Given two estimates of $j$, I wish to combine them using a normalised weighted mean, such that ...
6
votes
6answers
34k views

Sum of averages vs average of sums

I have essentially a table of numbers -- a time series of measurements. Each row in the table has 5 values for the 5 different categories, and a sum row for the total of all categories. If I take ...
7
votes
1answer
10k views

Average percent increase not equal to total percent increase?

I tried searching around for this but it was difficult to boil down the search terms. Plus nothing seemed to be showing up anyway. What's an easy way to show that the average percentage increase of n ...
2
votes
0answers
485 views

How can I compare two averages of imperfect measurements, with their std. deviations?

I have a process by which I measure the times it take to do something, (run some code), and this time varies, a lot. I'm trying to optimize this code, making small changes that sometimes have small ...
0
votes
1answer
196 views

Calculate average time

I have a huge list of times and would like to calculate an average or typical time. If I would just use the median (or other "normal" types of calculating an average), for example 23:59 and 00:01 ...
31
votes
3answers
44k 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 ...
0
votes
2answers
197 views

Calculating Average…

I know its simple problem, but i want to know if it can be solved some other way around.Here goes the problem. Input: 234 , 54678 , 34987 Problem is to calculate how many of the numbers(by number i ...
2
votes
2answers
291 views

Probability cut-off

Is there a probability cut-off point? e.g. if the probability of something keeps halving do you stop at a certain point and say the rest of the possibilities are negligible? What do you do then? ...
3
votes
2answers
306 views

Course Grade - Statistics Question

I'm confused about finding the standard deviation of various weighted objects in a problem. For example, consider an academic setting, with four assessments as follows: ...