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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3
votes
2answers
114 views

In what sense is the “average” of $sin(x)$ equal to 0?

I think it makes intuitive sense that if a phenomenon is described by simple sinusoidal oscillation, it is "on average" equal to its midrange, but I think I failed in trying to make that statement ...
-1
votes
1answer
38 views

One number to represent the percent changes of multiple numbers

Question: Is there a way to represent the total percent change of multiple numbers (make it into one number that represents change) that isn't just the percent change between the first and last number ...
0
votes
0answers
10 views

Probable minimun of a set having only Maximum, Average and the number of values

I have a data set in which I am given the number of values, the average and the max, how can i work out the probable min value? Thanks
0
votes
0answers
27 views

What type of function is F?

Suppose that $ X= \{(x_1,d_1),(x_2,d_2),...,(x_n,d_n)\}$ where $x_i$ for $i=1,...,n$ are variable and $d_i$ for $i=1,...,n$ have constant values, then we define: $$F(X)= \sum_{i=1}^{n}(\frac{ x_i} {...
0
votes
0answers
82 views

Calculating percentage of range of values given total set members and average (review ratings)

Given the total number of members in an unknown data set, with values ranging from a minimum of 1 to a maximum of 5, is it possible to determine the probable percentage of values that fall within a ...
1
vote
1answer
26 views

Weighted average of multiple angles

This answer has a good approach to calculating the average between multiple angles: simply convert each angle to its unit vector, add them up and convert the resulting sum vector back to an angle. The ...
3
votes
1answer
81 views

What about $\lim_{n\to\infty}\frac{\sum_{k=1}^n s_k\mu(k)}{n}$, for the zeros of Dirichlet eta function $s_k=1+\frac{2\pi k}{\log 2}i$ with $k\geq 1$?

Let for integers $k\geq 1$ the corresponding zeros of Dirichlet eta function of the form $$s_k=1+\frac{2\pi k}{\log 2}i,$$ then we can consider the following puzzle, when we multiply previous ...
1
vote
1answer
28 views

What is the proper notation for the “average of the last N elements of a sequence”?

I use sliding window average in my calculations: average for the last N elements and average for the N elements before that. What would be the correct mathematical notation to describe this?
1
vote
1answer
318 views

Aggregating standard deviation to a summary point

I have a range of data (server performance statistics) is formatted as follows, for each server: ...
0
votes
1answer
8 views

Finding the measured average angular velocities

Supposed I have a couple rows of data with recorded measured ratios $\omega_f/\omega_i$ and they ask me for the "Average Measured $\omega_f/\omega_i$ " This may seem like a really trivial solution but ...
0
votes
0answers
12 views

Calculate portfolio weighted averages - smoothing curve

I'll first off apologize for not knowing how to ask this question properly, but I just can't come up with the right words which is likely why I can't find an answer. I have a fairly simple portfolio ...
0
votes
1answer
19 views

the average growth rate/ Calculate the annualized return for the entire period

The returns from an investment are $2\%$ in Year $1$, $5\%$ in Year $2$, and $21.8\%$ in the first half of Year $3$. Calculate the annualized return for the entire period. I know the average growth ...
2
votes
1answer
31 views

Two player game about maximizing earnings subject to an interesting condition

Me and my friend had a bet. We each pick an integer between $1$ and $100$ inclusive and reveal it at the same time. Whoever picks the higher number has his number halved. Then the person whose number ...
0
votes
1answer
42 views

Factors that Impact a Weighted Average the Most

I am trying to determine how to calculate the factors that have the most significant impact on a weighted average. For example, let's say I am reviewing the number of patients that responded to a ...
0
votes
2answers
41 views

A mixture of two kinds of beef has a total fat content of 8%; find the ratio of the mixture

I am struggling a bit on weighted average problems on the GMAT. I'm a bit confused as to how they work and the best way to solve them. I'm kind of relying on intuition, but I'd like a more formal way ...
1
vote
1answer
55 views

Can you determine the average second derivative from a set of points?

Let us say we have a smooth function $f$. We can find the exact average of $f'$ on the interval $[a,b]$ via $$\bar{f'}=\frac{f(b)-f(a)}{b-a}$$ My question is, can you find the exact average of the ...
1
vote
1answer
49 views

Propagation of Uncertainties [closed]

I have five values for the volume of sodium hydroxide needed to neutralise a fixed quantity of hydrochloric acid, each trial with an uncertainty of 0.05 mL. If I take the average of these five values, ...
-1
votes
1answer
38 views

The average of 11 results in 50 [closed]

The average of 11 results in 50.If the average of first six results is 48 and that of last six 51,the sixth result is?
0
votes
0answers
26 views

Weighted average of slope

I'm trying to find the weighted average of a temperature increase in a vessel. So, essentially the weighted average of a temperature over time. I'd like some input if this equation gets me what I'm ...
1
vote
0answers
23 views

Advise on Weight Function for statistical analysis needed

I'm doing a statistical analysis of an experiment I'm conducting, and right now I'm trying to define a proper methods for data mining. Please take a look at my problem: I'm doing a user research ...
2
votes
1answer
39 views

Average velocity of fluid flow

Washburn equation for fluid flow in horizontal capillary is given by : $\frac{dL}{dt} = \frac{γR}{4µL}$ Find the time dependencies of length of travel, $L(T)$ and average velocity. I can find the ...
0
votes
0answers
19 views

Weighted rating value

I have a database consisting of clubs and its ratings people have provided them with. Currently, I am performing an average of the ratings based on a club and then sorting these averages ...
0
votes
0answers
28 views

Which is the default Standard Deviation Formula

I have to implement a test from research paper which says: As for testing criteria, standard deviation or min-to-90th percentile ( ) of large packets (1500 B) can be effectively used to find the ...
0
votes
0answers
8 views

Graphical Representation of the Risk over different aspects

I am having the Risk Factors which are from more than one assessment. want to show the Risk of the all assessment for year 2015 or any Month of 2015. all risk factors can be the part of any of the ...
1
vote
0answers
23 views

Calculating Weighted Averages – selecting a correct numerical scale for several variables

I have the following variables that i am going to use to calculate a weighted average: Variable Format Weight applied (out of 1) A Percentage 0.2 B Percentage ...
1
vote
2answers
119 views

Finding average of denominator knowing average of numerator and average of fraction [closed]

Good day to you all. I have a little problem I have been banging my head on for a while. I have come to think that it is impossible, but I hope you can save me. I have a fraction, $ \frac{num_i}{...
0
votes
1answer
25 views

Weighted average of household size given number of households of each size

I hope this isn't too simple to bother you with, but this calculation is at the center of a dispute at work and I want to make sure I'm on solid ground here. To begin with, we know that the average ...
0
votes
2answers
23 views

Average of two trips

Question While Driving from City A to City B,a car got 22 miles per gallon and while returning on the same road, the car got ...
2
votes
1answer
40 views

Is not always the accumulated probability until the expected value equal to 1/2?

My problem is that doing calculations with exponential distribution, the result I get is not 1/2, and I think it should be that according to the intuitive concept of the expected value. The density ...
0
votes
1answer
62 views

Determine skewness if only mode and median given?

For a given set of data the mean is 10.5 and the mode is 9. What c an we deduce about the skewness of the data? A The data is positively skewed. B The data is negatively skewed. C The ...
0
votes
0answers
14 views

Potential Reward Average

I'll try to get straight to the point. I'll be offering a reward system as part of a marketing scheme and it will be for a select amount of users who opt-in. What will be calculated is the overall ...
0
votes
0answers
22 views

What are the different ways to do a rating in a web application?

I tried to do an example using Bayesian Average in order to find the rating for 3 hotels. Following is my example, Hotel A 3 Votes/ 2 Star/ 1 Star,Rating- 3 Star Hotel B 1 Vote, Rating -5 Star ...
0
votes
1answer
18 views

Problem finding the median when using frequency tables

My question concerns finding the median from a frequency table. It only occurs if you have even amounts of data. My problem is this if I had 40 bits of data in a grouped frequency table the middle ...
0
votes
1answer
21 views

Unusual Weighted Average Calculation

Unfortunately I don't know the term for what exactly I'm looking for. I hope you guys can direct me. Problem at hand: Have a composite score for an employee performance, for example a score may ...
0
votes
1answer
18 views

Finding the average when two infos on averages are given

This is one competitive exam's question. Can someone give me an easy explanation on how to solve this problem? Question Sam earned a $2000 commision on a big sale,...
1
vote
3answers
315 views

Possibility that two students answer the same on a 25 question multiple choice test

I am trying to get some approximation of the possibility that two students would answer $25$ questions in a row exactly the same. There are 4 possible responses for each question. I calculate the ...
0
votes
1answer
26 views

Upper bound on an expectation

I'm looking for an upper bound on $E(X^k)$ where $X$ is a random variable with $E(X)=1$. How can I go about doing this?
2
votes
1answer
23 views

Extrapolate data points from a series of averages

Given a series of data points: $$\begin{array}{c|c|c|c|c|c|c|c|} & \text{Monday} & \text{Tuesday} & \text{Wednesday} & \text{Thursday} & \text{Friday} & \text{Saturday} &...
0
votes
0answers
33 views

Functions like EWMA

I have a problem in which a threshold triggers an event. I want to estimate that threshold dynamically as I get more information progressively. Exponentially Weighted Mean Average is one such ...
3
votes
2answers
120 views

Very fascinating probability game about maximising greed?

Two people play a mathematical game. Each person chooses a number between 1 and 100 inclusive, with both numbers revealed at the same time. The person who has a smaller number will keep their number ...
1
vote
1answer
22 views

Average distance to the closest neighbor

Suppose that 3-dimensional space contains countably infinite number of randomly positioned particles (points), on average $1$ particle per a unit of volume. Their distribution is homogeneous and ...
2
votes
1answer
153 views

How to calculate the average distance between two points in concentric annuli

I tried to solve this analytically but gave up and ran a simulation. I would still like to know if it can be done explicitly. Consider a circle radially divided into 'zones', so say zone 1 is the ...
1
vote
1answer
15 views

Difference between Means is the Mean of the Differences

Suppose you have a sequence $a_{1}, \dots, a_{n}$ and another sequence $b_{1}, \dots, b_{m}$, where $n$ and $m$ may differ. I want to know whether the difference between the arithmetic means of these ...
0
votes
0answers
38 views

sum of the log over the log of the count (Average of probablities)

I wondering if anyone has seen this "averaging" technique before, and what its advantages might be? The values being averages are probabilities and as such have a value of 1 or less. $\frac{1}{log(n)...
2
votes
0answers
40 views

Flat Tax vs. National Income Tax Average

If the national income tax average under a progressive system is 30%, will tax revenue change if the progressive system is changed to a flat tax also at 30%? In other words, if the mean average ...
0
votes
1answer
71 views

Interesting Original Probability Question

I have 100 balls, which are all initially yellow. Every minute, I randomly choose a ball and paint it red. How many balls are expected to be red after 100 minutes? Note: I could pick up a ball that's ...
0
votes
0answers
41 views

Number of meetings needed for everyone to know everyone

There are 100 people on an island. Each person has an unlimited number of name-tags with his name on it. (Everyone has a different name) When two people meet, each gives the other an unlimited number ...
0
votes
2answers
54 views

Question about the average number of cycles? [duplicate]

I have 100 cards labelled from 1 to 100. I place this in a row with all the cards face down. On the first turn I flip the first card. Now this card has a number $n$ on it. I then put this card face-up ...
44
votes
3answers
1k views

Expected number of people to not get shot?

Suppose $n$ gangsters are randomly positioned in a square room such that the positions of any three gangsters do not form an isosceles triangle. At midnight, each gangster shoots the person that is ...
1
vote
3answers
85 views

What is the expected value of this random number?

Suppose $a$ is a random number between 0 and 1 and suppose $b$ is a random number $\in (0,1)$ also. What is the expected value of $a^b$? (i.e. If I performed this operation $n$ times, what would be ...