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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45 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
25 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
38 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
85 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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0answers
72 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
34 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
16 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
72 views

Average distance from center to random point in rectangle

I need to find average squared distance from center in rectangle. One edge is 2, other one is 1. On my understanding I need to find $$E[X^2+Y^2]$$ So I got ...
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1answer
146 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
29 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
57 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
50 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
115 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
72 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
22 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
44 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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372 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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33 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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0answers
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
918 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
171 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 ...
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1answer
36 views

How to find the average in the given labels?

I generated 11 random variables follow the Poisson distribution. I used lambda equal to 5. The data that I got is following : 0.00673794699908547 0.0336897349954273 0.0842243374885683 ...
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1answer
50 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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0answers
51 views

Deconvoluting linear combinations of unknown distributions

Summary I am trying to deconvolute the distribution $T(x)$ of a population's $x$ parameter into sub-distributions ($P(x)$, $Q(x)$, $R(x)$ ...), of which I don't know the form (only that they have ...
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1answer
40 views

Generating statistics from data samples, that are of snapshots.

My question is part math part computers but I need more of the math answer then a computer answer. I am going to be grabing snapshots of a moment of time on how a computer is performing. Because of ...
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1answer
180 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: ...
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1answer
158 views

Estimating a sample mean using sub-sample means

we collect a lot of data on a daily basis via an API, and part of this data includes fields that represent sample means. Specifically, we get provided with a sample mean and the sample size, lets call ...
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1answer
68 views

averaging STDs vs. calculating a single STD

I have a set of data points. I extracted the Standard Deviation for the whole set, and also extracted STDs for a partition of the points where each element of the partition has at least two points. I ...
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0answers
54 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 ...
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30 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 ?
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1answer
48 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 ...
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2answers
64 views

Average of percentage of 2 numbers.

If I have 24081 items sold at 45% off. and 11386 items sold at 60% off. What is the average percent off for all items sold? Thanks for your help in advance! Craig (This is not homework :) )
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78 views

How to get the average of $a$, $b$ when all you know is the average of $a,b,c$ and the value of $c$?

I need to figure out some averages for some javascript I'm writing. The data I have is: I know the average of $a$, $b$ and $c$. I know the value of $c$. I do not know the values of $a$ and $b$. ...
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1answer
145 views

Getting Average

How excatly do I calculate the average? Can somebody explain step by step process of how to get an average? If I have an array of numbers (5, 3, 4, 3, 1) and so on. And I need to get the average of ...
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2answers
95 views

Average Proofs, where $n\ge 2$ is greater than the average of real numbers

Prove that at least one of the real numbers $a_1; a_2;... a_n,$ where $n \ge 2$, is greater than or equal to the average of these numbers. I'm stuck on how I am supposed to prove this. Honestly ...
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2answers
156 views

Effect of removal of numbers while calculating average

My question is , lets say we have the numbers 1,2,3,.....,n numbers . 2 consecutive numbers are removed. The avg of the numbers after the removal of numbers be m let the numbers removed be k,k+1 ...
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5answers
451 views

Is this a weighted average/percentage problem?

Let's say a Marketing company has a total turnover of 10000 \$ There are 3 salesmen A,B,C with the following turnovers A = 2000 $ B = 3000 $ C = 5000 $ Now, ...
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6answers
42 views

Confusion (Averages)

I'm getting insanely frustrated with this. The average of $6$ numbers is $4$. A seventh number is added and the new average is $5$. What is the seventh number? How do I solve this algebraically? $6 ...
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3answers
29 views

Average speed question of a car on an oval track

On an oval track, a car averages $30$ M.P.H. (miles per hour) for the first lap (a lap is $1$ mile around the track). At what average speed must that same car drive the 2nd lap on that same track so ...
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1answer
443 views

Working with average numbers and finding unknown variables?

There is this question I was approached with and I am absolutely stumped on where to even begin to solve it. It goes like this: Based off the following 4 equations, find the average of $x_1$, $x_2$, ...
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2answers
145 views

given average score,find the selected numbers

Suppose average score of 46 scores selected from 1,2,3,4,5 is 1.65.Is there any way to find out which are the scores that are selected.
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21 views

Minimum Value Given Average

I am struggling with this (very embarrassingly basic) minimization problem: I have the answer, which is great, but I'm oblivious as to how to go about solving this short of using calculus. The ...
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1answer
26 views

Average of Numbers

Consider the following problem: if $a \leq b \leq c \leq d \leq e \leq f \leq 101$ and if average of these(a,b,c,d,e,f) numbers is 100 then what could be the least value of a?
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61 views

Computing the average difference in a list of numbers

I have a list of numbers 280, 449, 689, 959, 1360, 1740, 1139 so there is between 289 and 449 is a distance of 169 and then between 449 and 689 a distance ...
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3answers
44 views

Help with question about Normal distribution

The heights of people at some city is $N(\mu,\sigma^2)$. 25% of the people are above 176 cm. and 20% are below 165 cm. How do I found $\mu,\sigma^2$? We choose randomly a group of 100 people. What ...
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1answer
37 views

Average value calculation

A company has 2 mines: A and B. The production per person in mine A was 22,6 tons last year, and 27,9 tons in mine B. Last year 60% of the total production came from mine A. The question is the total ...
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2answers
17 views

Is there a formula for finding the series of numbers based on an average.

So I am working on a program that does a scrolling effect. the image is 1200pixels wide, and each time it scrolls, it should move an average of 2.67 pixels. However I am using a function that does not ...