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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2
votes
2answers
23k views

What is the difference between the normal average and weighted average?

What is the difference?For what kind of purpose do we use the weighted average method?Why don't we instead always use the normal average method?and also,how to get the weighted average of some numbers?...
26
votes
4answers
11k 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 ...
3
votes
3answers
3k views

what does `ensemble average` mean?

I'm studying this paper and somewhere in the conclusion part is written: "Since this rotation of the coherency matrix is carried out based on the ensemble average of polarimetric scattering ...
1
vote
1answer
428 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 ...
1
vote
1answer
33 views

Which is the proper way to calculate average speed.

Let's say we have a graph, a distance-time graph, and there are couple points on the graph. The points are connected to each other with different slopes, so with different speeds between the points. ...
0
votes
1answer
22 views

Detecting unusual activity

How would one go about detecting unusual order flow in an intelligent way. That's very broad, so let me narrow it down. I have a trading system with clients entering number of orders every day. At ...
0
votes
1answer
10 views

Calculating the average with Limited memory and without using the count

I am having a flow of numbers on an embedded device, and I cannot store the flow of numbers and would like to calculate the average. I have checked around and found one way was to do like this Avg= (...
6
votes
4answers
16k views

what is the difference between average and expected value?

I have been going through the definition of expected value in Wikipedia (http://en.wikipedia.org/wiki/Expected_value) beneath all that jargon it seems that the expected value of a distribution is the ...
5
votes
1answer
235 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 7:...
0
votes
0answers
8 views

Weighted mean / average where you reward the lowest value - cost - distance

Best I've several weather-station (200), placed across the country (508 municipalities). Now, I would like to prescribe the weather info, e.g. temperature, to each of the municipalities of that ...
1
vote
0answers
28 views

What do attendance figures tell me about regularity? What does the average tell me about individual attendance?

Suppose I have a group of $N$ people, attending a series of $M$ events, and (for simplicity) let's assume the overall attendance happens to be the same at each event, say $A$ people (ranging between 1 ...
1
vote
1answer
22 views

Variance of exponential moving average

I'm not quite sure what the form for the rolling recursive variance should look like. I have that the recursive average is $m_t = \alpha x_t +(1-a)m_{t-1}$. Then would the rolling recursive variance ...
1
vote
0answers
28 views

Exponential smoothing and variance

I have a time series, let's denote it as $X_t$ (a series of prices). We exponentially smooth the data to obtain another time series, an exponential moving average: $EMA_t$. My question is how do I ...
3
votes
3answers
105 views

Average value of $e^{-x}$ from $0$ to $\infty$

I just signed up for this site so I hope I'm doing this right. I've been having trouble wrapping my head around the average value of the function $e^{-x}$ from 0 to $\infty$. I know that the average ...
0
votes
0answers
238 views

How to find the average velocity of blood?

The velocity $v$ of blood that flows in a blood vessel with radius $R$ and length $L$ at a distance $r$ from the central axis is $$v(r) = \frac{P}{4\eta L}(R^2 − r^2)$$ where $P$ is the pressure ...
1
vote
1answer
14 views

Average amplitude of the sum of N sines with random phase differences

We have N functions of the form $asin(kx+c)$ Their $a$ and $k$ values are the same their $c$ is a random number between $0$ and $2\pi$ $f(x)$ is the sum all N functions I know $f(x)=Asin(kx+c')$ ...
1
vote
1answer
407 views

Calculating average customer turnover

I am currently coding a script which displays data for a company intranet. I am stuck with a question that seemed pretty simple, but turned out to give me headaches. We have the following scenario: ...
0
votes
2answers
28 views

Volume and Average Height

How do you calculate the average number of floors of buildings across a city block when all the buildings are varying heights. Followings in a listing of what the area looks like and the number of ...
0
votes
0answers
36 views

How can I calculate accuracy of an estimate based on a subset of data?

For example, say I'm trying to determine the average number of steps taken in a day for a population of 100M people. I know the exact number of steps for a random 25M subset of the 100M group (2500 ...
-1
votes
1answer
21 views

How can I get the average angle from a set of three points?

Please forgive me, but I'm not mathematically inclined and i'm trying to solve a problem for a video game i'm developing. My levels are composed of vector shapes and i want to find out what the ...
0
votes
0answers
10 views

Normalize and Average weighted

Everyday I receive a data of three variables (neutral, negative and positive). ...
0
votes
0answers
20 views

Boosting v. weighted average

I have been watching an MIT online Artificial Intelligence lecture by Prof. Winston about boosting. The boosting technique uses complicated maths to combine the results from several weak predictors to ...
14
votes
3answers
404 views

If my average speed is 50 mph, is it better to go 10% faster or 5 mph faster? (These are not the same)

BACKGROUND Suppose we have a journey between $A$ and $B$ where different sections of roads have different speed limits and our average speed is $50$ mph. If when I repeat the journey I travel $10\%$ ...
2
votes
0answers
42 views

What is the average maximum value of a set of random numbers? [duplicate]

Let $a_1, a_2, a_3, \ldots, a_{10}$ be ten randomly chosen real numbers in the interval [0,1]. Let $m$ be the maximal value out of these 10 numbers. What is the expected value of $m$? (i.e. If i ...
0
votes
0answers
25 views

Anyone have any good ideas on how to average 2D directions?

Directions, being a cyclical quantity (i.e. if you keep increasing the value, you'll eventually end up back where you started) can't be averaged out like regular numbers. For example, say I have 2 ...
0
votes
0answers
17 views

The average value of f on region R (double integrals)

If I am given f(x,y) and I calculate the average of the region given by the formula in this image should the average always = (min of f(x,y) +max of f(x,y))/2. I think this is only the case if the ...
0
votes
0answers
33 views

How can I calculate my current average for my class?

I'm trying to do some what-if scenarios for one of my courses and I'd like someone to double check my work. The grade breakdown is as follows: ...
0
votes
2answers
45 views

How do I calculate a combined data error?

I have a time series of data points read from an instrument, I also get an estimate of the error ($\sigma$) for each of these readings. e.g. $10.12 \pm 0.05$ $10.09 \pm 0.02$ $10.20 \pm 0.12$ ...
-1
votes
1answer
19 views

Buying forecast

I have a set of items. In 2013, I bought x of a certain item, in 2014 I bought y, and in 2015 I bought z. In many cases, I only bought the item in one year, like: ...
0
votes
1answer
55 views

What is the name of this formula??

Let formula_a = lambda array: sum(array) / len(array). We may rename this formula to be average or ...
1
vote
1answer
16 views

How is the first term weighted in an exponential smoothing, or exponentially weighted moving average?

I'm working with exponential smoothing for a series, using the formula $z_i=\lambda \bar x_i + (1- \lambda) z_{i-1}$, as explained in this wiki article. Using this method, should $z_{1}$ be defined ...
0
votes
0answers
21 views

How do you set the half-life of an exponential weight?

I'm trying to follow the process described in a paper, where they smooth a time series using exponential weights, for which I'm using the formula $z_i=\lambda \bar x_i + (1- \lambda) z_{i-1}$, as ...
2
votes
3answers
1k 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?
1
vote
0answers
17 views

Confused by simple risk problem

I am having troubles understanding this basic problem and would like to see if anyone could help me out. I have two boxes: one red, one blue. Depending on what box I pick, I have the potential to ...
0
votes
2answers
41 views

Bit increase when averaging?

I have a given number $N$ of binary numbers, that are stored using a given number $B$ of bits. $B$ is the same for all the numbers. For example, thease values where $N = 4, B = 4$. ...
0
votes
0answers
16 views

Can distributions scale to any given time scale?

I am working with some colleagues to set up alerts based on call center data, and I feel that something is wrong with how it is currently being done, but I'm not sure what exactly, or how to explain ...
0
votes
1answer
25 views

Applications of mean and standard deviation

If I have this set of numbers: [9,7,5,5,4,4,4,2] We know that: mean = 5 variance = 4 standard deviation = 2 But is there an application/formula of standard ...
43
votes
3answers
72k 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
1answer
25 views

The average of 38,84,63,45,32 and n lies between 50 and 60.If n is an integer greater than the average of the above numbers, then n lies between?

The options are 53 < n <97 50 < n < 100 52 < n < 98 I added the values along with n to get 43.66 + n/6.I then tried plugging in values from the options and tried arriving at ...
0
votes
2answers
43 views

A worker is told that only $5\%$ of all workers make a higher wage. If the wages are normally distributed, what is the average hourly wage?

So let's say a worker earns $\$16$ per hour at a plant and is told that only $5\%$ of all workers make a higher wage. If the wages are normally distributed with standard deviation of $\$5$ per hour ...
0
votes
0answers
16 views

How to determine a formula for an index of compliancy

I hope you will be patient with the inarticulate question of a non-mathematician. It's hard to get an answer when you don't even know how to ask the question. Here the contest: Let's say that I have ...
0
votes
2answers
35 views

Average time between successive occurrences of earthquakes?

In any given year, the probability of an earthquake greater than Magnitude $6$ occurring in the Garhwal Himalayas is $0.04$. The average time between successive occurrences of such earthquakes is ____ ...
1
vote
0answers
17 views

Average Value of a Line Integral

I'm having quite a hard time calculating the average value of a line integral. Given the surface $f(x,y) = \sqrt{16 + 36y^{2/3}}$ and the curve $y = x^{3/2}$, I need to calculate the average value of ...
0
votes
1answer
35 views

Average cost of units over time

I buy and sell units at varying price and I always have a varying stock of units bought in different batches at different prices. I always keep the current_price and the current_volume and I base my ...
6
votes
7answers
48k 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 ...
0
votes
0answers
9 views

Average discount give for product line

I have been out of school for entirely too long to remember how to build this equation. I am trying to calculate the average discount given for our entire product line, that is sold over 4 distinct ...
2
votes
3answers
2k views

Way to aggregated percentiles

I want to have information of http response times. The average, 95 and 99 percentil. All the response times are collected in each web server, and every second is sent back to a central server that ...
0
votes
1answer
34 views

Function to determine a set of numbers are balanced

Given the following data, based on a 0-100 scale ...
2
votes
2answers
36 views

Is there a name for the way I am averaging the cost of cards?

My buddy and I were discussing different ways of deciding how much mana to include when constructing a deck. Without thinking much about it I used a method of finding the average converted mana cost ...
2
votes
3answers
58 views

Determining the Average number of Attempts before a result occurs (using defined Probabilities)

I'm trying to solve this problem but I'm completely unsure of what sort of concepts/formulas/proofs I need in order to tackle it. I'm just lost on where to start. Here's an example story problem as it ...