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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18 views

Averaging percentages of events occuring

You have $8$ possible events that could occur in a given day. Out of $21$days, only one event occurred once, two and three events occurred $9$ times each, four events occurred once and seven events ...
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3answers
82 views

Difference between these two standard deviation formulas?

Today I started reading statistics and I came across these two S.D formulas: $$\sqrt{\frac 1 n \sum (X - \overline X)^2} \textrm{ and } \sqrt{\frac 1 {n-1}\sum (X - \overline X)^2}$$ What is the ...
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1answer
75 views

Can the norm of a convex combination of vectors be greater than the norm of their sum?

Can the norm of a convex combination of vectors be greater than the norm of their sum? Or is it always the case that: $|| \sum_i w_i x_i || \leq \sum_i w_i \;|| \sum_i x_i || $ (for positive ...
1
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1answer
92 views

Average difference between consecutive data

I have in my head a very simple concept, but it's difficult to search for. I feel like there must be a function for this in statistics, but I have no idea what to look for. I have a 1 dimensional ...
0
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0answers
11 views

Dividing a segment into intervals. [duplicate]

I want to divide a segment of unit length into three intervals by selecting two distinct arbitrary points on the line segment. If I do this, what is the expected value of the smallest/shortest ...
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1answer
153 views

How to calculate the average x-coordinate of a region?

I have a region in the x-y plane. Now I randomly select a point inside or on the boundary of the region. What is the expected value of the x-coordinate of my point? I.e. If I perform this operation ...
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1answer
205 views

Determine “average min and max” of a list of values

I've got a large dataset of about 1,000 values which represent the flex of a finger (higher s more flexed). The data is collected within 10 seconds. During that time the finger will be repeatedly ...
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1answer
54 views

Calculating the average of percentages from fields which have a “weight” multiplier applied.

This is for some software I'm writing. I have a number of fields, all of which have a score input which allows a percentage of 0-100. Each field has a "weight" property, which determines its ...
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2answers
32 views

Define temperature by clustering with math operators

I can´t figure out how to cluster the temperature for the weather in 3 optimal cases: hot, mild, cold My data contains: air temperature(the average daily value), max air temperature(highest daily ...
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0answers
28 views

Finding average as well as impact of quantity

I am new to this site, I am basically a developer and stuck at a logical mathematics portion. I have polarity of people sending email, so suppose p1 sent mail and mathematical polarity came out to be ...
2
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1answer
75 views

Average of a list of numbers, read one at a time

I have a dilemma Lets take the set $\{1, 2, 3, 4, 5, 6, 7, 8, 9\}$ If we wanted to calculate the average of this set we would add up all the numbers in the set $(45)$ and then divide by the total ...
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0answers
17 views

How can I calculate percent error with a denominator of 0? [duplicate]

I am using the MAPE formula, ABS(actual-forecast)/actual *100, but this raises problems when the actual values are zero. Is it possible to add 1 to the denominator and calculate this way? Would I get ...
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1answer
52 views

Could someone explain the notation of the average of quaternions equation?

The equation has some notation that is difficult to find the meaning for. It is equation (3) in the paper 'Quaternion Averaging' by F. Landis Markley, et al. on page 3 under 'The Average Quaternion'. ...
1
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1answer
47 views

Why this process is nonergodic?

I am studying a tutorial on stochastic processes and there's an example in it which I don't understand anything of it. First of all there is this criterion for a mean-ergodic random process: For ...
2
votes
1answer
37 views

Is tossing a die in 10 consequent days an ergodic process?

IT maybe an elementary question but I'm totally new to the concept. In Wikipedia, ergodicity is defined as follows: In statistics, the term describes a random process for which the time ...
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1answer
42 views

what's the difference between variable and process from a statistical point of view?

I'm reading a tutorial stochastic process: ergodicity and temporal averages and I'm totally confused. It is said that: Suppose an IID random process whose marginal PDF is Gaussian with mean ...
0
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0answers
57 views

what is the difference between statiscal averagre and average?

I'm reading a book on synthetic aperture radar and it is said that: The term $\sigma^{\circ}$ is the averaged radar cross section per unit area, also called the scattering coefficient or ...
0
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1answer
126 views

Combining percentages differences

I would like to know the difference between two approaches of combining percentages. I found an online example that match my situation; the example have been found in The University of Georgia page. ...
1
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1answer
79 views

How to summarize a big table of results? Average or Geometric mean?

I am writing a paper for a Computer Science conference and I have a big (way too big) table of results (times and some other measures) for different versions of an algorithm. I would like to summarize ...
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2answers
59 views

Average value of distinct combinations

Distinct combinations of 123 are 123, 132, 213, 231, 312 & 321. Adding those and dividing by 6 gives the average 222. Same goes for 246: 246, 264, 426, 462, 624 & 642. Added up and divided by ...
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2answers
70 views

Difference between the two ways of finding average winning rate over a period of time

Ok I might be asking something stupid, please bear with me, math is not my strong suit. This has to be a duplicate but I dont know how to search them. I dont even know how to word the title, kindly ...
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2answers
52 views

A specific kind of Moving average

The problem is : Consider the list consisting of the first n natural numbers without zero, ie from $1$ to $n$. We define the transformation "moving average" on the list of $n$ elements by ...
4
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2answers
131 views

Average $lcm(a,b)$, $ 1\le a \le b \le n$, and asymptotic behavior

What is the average value for $\mathrm{lcm}(a,b)$, with $ 1\le a \le b \le n$, for a given $n$, and what is the asymptotic behavior? The $\mathrm{lcm}$ is the least common multiple. I have ...
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1answer
108 views

Average score for a Quiz based on recent performance

A quiz always has 10 questions. Correct answer results in 1 mark. No negative marking. A user can take the quiz as many times as he likes. I want to show his 'Average Score' based on last 5 quiz ...
2
votes
1answer
76 views

Why is the average of a sum equal the sum of the averages?

I came across this website showing the proof of the above question in the Expected Value section. However, I do not quite understand why the probability of $xy$ becomes the probability of $x$ (or $y$) ...
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1answer
44 views

Intuition: Average vs. Average Rate of Change

I intuitively understand the examples below, but I don't see an "average" in the average rate of change (I see a ratio of two delta values). What is the relationship between the average (arithmetic ...
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1answer
12 views

Grading limitless variables

I am trying to calculate the quality of a triangle. Parameters are skewness, aspect ratio, and size. Skewness ranges between 0 and 1. Aspect ratio is the ratio of longest edge to shortest edge. ...
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0answers
8 views

How to show monotonicity of this weighted average?

I have a sequence of positive and increasing (in all of its arguments) functions , $\{f_i(x_1, x_2, \dots, x_M)\}_{i=1}^M$. I also have: $$ ...
2
votes
2answers
105 views

weighing avg by columns vs rows outputs different results

First of all, I just know the basics of math, so please be patient. I have an overall score for a company with the product1 and product2. However when I do the overall for each criteria like ...
-1
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2answers
38 views

Average Attendance [closed]

I need to find a monthly average attendance. 3 out of 4 weeks were not counted. Do I take the number from the one week that was counted and divide by 4 or just use that one number as the average?
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0answers
31 views

Understanding the convolution as a weighted average to eliminate noise $ s(t) = \int x(a) w(t-a) da$

I was reading Yoshua's Bengio [book][1] on convolutional neural networks and it has small section that described/explains the convolution in the context of estimating the location of a spaceship with ...
3
votes
1answer
48 views

Expected value (mean) of function from polyline

Suppose we have a polyline that has such properties: It consists of n segments First segment's ends are (0, 0) and ...
1
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3answers
43 views

how do they calculate these following columns

I have these data: I am sorry the data is in Portuguese, and it is an image so I can't convert it to a table but the translate "probably" ( i am not a native speakers for Portuguese language) is: ...
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0answers
17 views

Moving average where periods have unequal # of samples

I'm trying to compare a simple moving average approach to one that normalizes by the number of samples in a period to determine which is "more correct." Here's a representative piece of the data: ...
0
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1answer
89 views

SAT Math Question Confusion

I was doing a practice new SAT Test and was wondering exactly what this question is asking and how it got to the answer. Thanks!
0
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1answer
66 views

Five-year Annual Average vs five-year Weighted average maintenance costs for two car types

If we are comparing maintenance costs (M$) per mile (M$/m = Mtype) of two car models over a 5 year period, where the number of cars that are type (a) is much less than type (b), and the number of type ...
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 ...
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2answers
812 views

Weighted Average Distance between 3 or more points

I'm trying to find out the average point between 3 or more points, given each distance that the end point is away from each of the other points. With 2 points it's easy, I believe the formula should ...
0
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0answers
86 views

List of graph data points, need accurate calculation/estimate formula for excel

So I'm working on a small project that will use a calculation in excel, I'm nearly there and the only piece missing is being able to accurately estimate a data point from the following set of data ...
0
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1answer
21 views

compute a value based on goegraphic range from measuement devices

Today is one of those days when the correct method to calculate this escapes me. I have 3 fixed points on a map where measurement devices are located. These all track the same transmitters. A mobile ...
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0answers
18 views

What kind of time series do I need?

I am trying to optimize a list of websites on which to purchase banner advertising using the following setup: For each banner ad impression I buy I am charged $0.001. When my ad is clicked it ...
1
vote
1answer
258 views

Average patients waiting time in dental office

At a Dental Office, patients come in at the rate of 20 per hour and, on average, are processed at the same rate. Patients wait in a queue till they are called up to the counter for registration. After ...
1
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0answers
41 views

Matlab, Extracting Particular Values from an Excel File

If I have a table of values in Matlab ( here I have a 40k rows, and about a dozen columns), how can I read only particular values from each row? My goal is to extract some of the values from each row, ...
0
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2answers
45 views

Explaining this inequality

In a proof I was working on today, I assumed this equation was true which lead to devastating results $$ \sqrt{\bar{x^2}} =\bar{\lvert x\rvert} $$ For instance, given the data 0 and 2, the left hand ...
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0answers
22 views

Averaging Models in Excel

I am working in Excel and have two sets of data points that come up with a percentage for the likelihood of a recession. I am wondering what the best strategy would be to combine these data points? ...
0
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1answer
80 views

The validity of dividing an average cost by an average duration?

Let's say you wanted to calculate, for example, the average (i.e. mean) cost per day for a hotel to accommodate a tourist. If only aggregate cost data is available, is dividing the average cumulative ...
0
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0answers
37 views

How do you calculate the weighting towards an average?

I guess in a way this is like calculating a weighted average, only backwards, i.e. from the average, we want to calculate the weightings Lets say there are two people A and B A's average call time ...
0
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0answers
82 views

How to calculate a weighted average over a closed surface ?

I'd like to understand a bit more the following problem. Suppose a potato shape (say a 3D volume bounded by a 2D surface), and define $n$ the normal vector to its surface, with components $n_i$. ...
2
votes
1answer
85 views

Average of elements in a subset of $\{1,2,3,..,n\}$ is greater than $\frac{n+1}{2}$ [closed]

Consider two integers $n \ge m \ge 4$ and $A=\{a_1,a_2,...,a_m\}$ a subset of the set $\{1,2,3,...,n\}$ with the property that $$\forall a,b \in A \text{ with } a \neq b, \text{ if } a+b \le n, \text{ ...
0
votes
1answer
6 views

Rate Times Distance Problem with Averages

On your drive to Hoover Dam, you maintain an average speed of 50 miles per hour on the way up. Returning home, you are only able to average 45 miles per hour because of heavy traffic. What is your ...