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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25 views

statistics z score

I'm curious what the phrase "on average" means. Here is an example: On average, 30% were further than ___ kilometers away when they had their accident. Is $30\%$ a $z$-score or is it a mean? ...
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1answer
40 views

Sum and sum of average not matching

I'm struggling with the following problem. I have a table showing the % of a population that like (say) bananas in three locations, the population of each location, and the total population who like ...
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1answer
160 views

Average value of a piecewise defined function

Consider the function $f$ defined by $$ f(x) = \begin{cases} x, & 0 \leq x < 1 \\ x^2, & 1 \leq x < 2 \\ \vdots \\ x^n, & n-1 \leq x < n. \end{cases} $$ I'm trying to compute ...
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174 views

Sum of weighted squared distances is minimized by the weighted average?

Let $x_1, \ldots, x_n \in \mathbb{R}^d$ denote $n$ points in $d$-dimensional Euclidean space, and $w_1, \ldots, w_n \in \mathbb{R}_{\geq 0}$ any non-negative weights. In some paper I came across the ...
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544 views

Mean/ Expected Value of $X^4$

$\def\Var{\mathop{\rm Var}}$Can anyone help me prove that Expected Value of $X^4$ is $3\Var(X)^4$, if the Expected Value of $X$ is zero and $\Var(X)$ is the Variance of $X$? Thanks!
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46 views

Expected average of number of tiles empty

I have a grid of 3x4 and every tile on the grid has a corresponding chance of being empty. This chance is given. For example, consider the following grid: $$ \frac{14}{15} \frac{1}{3} \frac{8}{13} ...
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569 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 ...
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1answer
819 views

Algorithm to separate an array of numbers into “low”, “medium” and “high” ranges

this is my first post on Math-Exchange. I'm a programmer, and I work with object-oriented algorithms, but when things gets too "algebraic" I get stuck. So I thought I'd ask over here. I need to ...
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1answer
106 views

averaging time it takes to complete a project

Consider a project consisting of four activities A, B, C, and D. a) A and B, the first activities of the project, can be started simultaneously. b) C can be started only after A is completed. c) D can ...
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2answers
144 views

Merging/averaging percentages

This may be a very simple question, but I'm not even sure what the correct terminology is for the procedure I am trying to do so I wasn't able to find anything else here... The scenario is that I'm ...
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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" ...
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1answer
212 views

Bound on deviation between arithmetic and harmonic mean?

It is well known that, if HM denotes the harmonic mean and AM the arithmetic mean, we have $$ AM(x) \ge HM(x) $$ Now I am dealing with the expression $$ \frac{1}{HM(x)} - \frac{1}{AM(x)} $$ A ...
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2answers
125 views

Probability of a normal random variable added to a number being greater than another normal random variable, and distribution of average

$X$= random height of a male $Y$= random height of a female $X$ and $Y$ are independent of each other For $x$, $\mu=180\text{ cm}$ and $\sigma^2= 16\text{ cm}^2$ For $y$, $\mu=170\text{ cm}$ and ...
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4answers
19 views

Percentages not adding up

I have a series of percentages: 132/220 (60%) and 88/220 (40%). Now when I break them down into subcategories and then recalculate the percentages them come out 5% different. 81/140 (58%) and ...
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3answers
64 views

Find the average test score for each of three groups, given overall averages

I've been working on this question for the last hour and cannot determine a solution. Q: 100 children, 200 teens and 300 adults write a test and an average is computed for all three groups. The ...
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2answers
39 views

Where should I use median instead of average?

Is there a general law, or rule of thumb, or rationale, when to use median and when average? Although I know the difference and how they are computed, when I try to translate to simple English I ...
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1answer
25 views

fast solve average

there are Indians and Europeans in an army of 12,000. the average height of Europeans is5'10" and that of Indians is 5'9" and the average height of entire army is 5'9,3/4. find out the number of ...
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1answer
37 views

Does missing a number from a set affect the average?

Firstly, apologies for an uninteresting title, and whether this is absolutely newbie maths. I'm a programmer, and when it comes to maths and me - the wheel is going, but the hamster is dead. On To ...
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1answer
66 views

Calculating the average of multiples and divisions

Imagine a number line that contains every value that is greater then (but not inclusive of) 0. The center of the line is 1. On the right side of the center(1), obviously, are all the whole and ...
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1answer
50 views

weighted average with exponential weighting

I want to create weighted average, where weights depend on value of number. If I want exponential weights is this regular? $average = \log_e(\frac{\sum_{i=1}^n e^{v_i}}{n})$ Isn't it just average of ...
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1answer
147 views

CAGR, log of negative numbers

I am trying to calculate the Compound Annual Growth Rate (CAGR) of a number of companies using the Geometric mean of the annual growth of their EPS. Some of the EPS values are negative(loss making) ...
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1answer
44 views

is this or (when) does this equality hold for weighted power series

$s_n=\sum _{k=0}^n a_k$ for every $n$ and $x\in(0,1)$. Let $p=(p_n)$ is a sequence of nonnegative numbers with $p_0>0$ s.t $P_n= \sum_{k=0}^{n}p_k \rightarrow \infty$ as $n \rightarrow \infty$ ...
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1answer
95 views

Vote “0-10” dignity.

I have this problem very difficult for me to solve. I have a company and some employees. Each of them expresses an opinion on some apples of varying quality. The vote can be: ...
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1answer
60 views

The Average Speed of an object

I'm pretty sure this has more to do with fundamental Math than Physics and that is why I'm asking this here rather than Physics.SE Imagine some object travelling along a straight path from point $A$ ...
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1answer
37 views

Statistics Range from x to y find average

The problem state that: Quantity A: The integer ages of the three children range from 2 to 13, and no two children are the same age. The average of all three children. Quantity B: 10 Compare A and ...
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3answers
57 views

Estimating $\sum_{k=1}^N a_kb_k$ given the means $\bar a_k,\bar b_k$ and determining the error

I need to calculate the following expression: $$\sum_{k=1}^N a_k b_k$$ I know the average values of $a_k$ , defined as $\overline {a_k} = {\sum_{k=1}^N a_k \over N } $ and $b_k$ , defined as ...
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2answers
372 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?
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1answer
38 views

For N-day moving average, how is N parameter called?

I'm looking for a good name for the variable. Average window length? Sounds like a term for a glass cutter.
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1answer
526 views

Weighted Average of Percentage Increases

I believe I have quite a simple problem, but want clarification on whether it is the best method to use. Say I have have insurance line, and the net income (£) from this business for 2011, 2012, 2013 ...
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1answer
455 views

Expected value of a multivariate distribution

Given this random vector: $$ \mathbf{x} = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} $$ And this probability distribution function that takes it as argument: $$ f_\mathbf{X}(\mathbf{x}) = ...
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2answers
121 views

Calculating new vector positions

I'm using the following formula to calculate the new vector positions for each point selected, I loop through each point selected and get the $(X_i,Y_i,Z_i)$ values, I also get the center values of ...
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1answer
232 views

Calculate vector position

I'm trying to calculate & move vertices to their average "radius" and form a circle from these new positions. Example: I have 8 vertices selected, I have a little script in Maya that will iterate ...
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1answer
244 views

Intuition calculating average price change

Given two products p1 and p2, each with a price per single unit and an amount per year. The question is to calculate the average change in price for both products combined. ...
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1answer
66 views

Calculating expected value

Here is the problem. In a game(shown below) with the marker in the center on each turn the marker moves to a neighbouring region with all positions equally likely and the player collects the cash ...
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2answers
707 views

How can I find the average y value of a function on a given domain?

Lets say that $f(x) = (10 - x)\ln x$. Over the domain: $1 ≤ x ≤ 10$. How can I find the average value of $y$ over this domain and what is that value?
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1answer
109 views

Derivative of a 'weighted average' of decreasing fractions

I'm having some trouble showing the following statement (which intuitively seems to hold): Suppose I have a series of fractions indexed by $i$ , each of them a function of $N:f_{i}\left( N\right) ...
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1answer
229 views

Minimum Numbers to find the given average.

Average score of the player (sum of scores in all the games / no. of games) is given. How Can we find the minimum number of games the player should have played to achieve that average. scores are non ...
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2answers
100 views

Maximum Profit at which combination

A dealer deals only in colour TVs and VCRs . He wants to spend up to Rs.12 lakhs to buy 100 pieces. He can purchase colour TV at Rs. 10,000 and a VCR at Rs. 15,000. He can sell a colour TV at Rs. ...
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1answer
253 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 ...
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1answer
142 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. ...
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1answer
108 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 ...
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1answer
240 views

math distribution of averages and distribution of standard deviation for comparison of bytes

Let me change my question: I have a sequence of 512 numbers (these 512 numbers can have a value between 0 and 255) (in computer mode these numbers can be between 00000000 and 11111111 (bits)). For ...
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2answers
35 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
14 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
79 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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0answers
19 views

Are these two approaches to calculating return rate mathematically consistent?

I have coded two C# programs, which use two different approaches to evaluate the outcome of a certain casino-style game (casino-style in the sense that the user pays points to take a turn, and ...
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1answer
45 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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2answers
33 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
15 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
67 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 ...