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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6
votes
1answer
188 views

Why is the $0$th power mean defined to be the geometric mean?

Mentioned in the wikipedia article, the $0$th power mean is defined to be the geometric mean. Why is this? I understand that a convenient consequence is that the means are ordered by their exponent. ...
1
vote
5answers
139 views

How do you determine the “average” of a certain value?

I have checked out the Wikipedia article, but it's too complicated for me. Also, this definition: constituting the result obtained by adding together several quantities and then dividing this ...
6
votes
0answers
199 views

What's the average distance between two discs in the plane?

Consider two discs in the plane of radius $r$ and $s$, with centers separated by a distance $l$. If we choose a point uniformly at random from each disc, what is the expected distance between the two ...
1
vote
1answer
34 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 ...
1
vote
3answers
52 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 ...
0
votes
1answer
23 views

What is the average value of number-range along interval?

Given a finite range of real numbers $$x = x_0,x_1,x_2,...,x_n$$ and an interpolation function $f(c), c\in[0..1]$ (such that e.g. $c(0)=x_0$, $c(1)=x_n$), and an interval $$I =[u,v], u\in[0..1], ...
0
votes
2answers
44 views

Average and aggregate values with a distribution function

I'm reading an economics paper and I'm trying to understand if a statement made by the author is an assumption or the consequence of a previous definition. The part I don't understand is the ...
0
votes
0answers
29 views

Does MACD have exact or approximate upper bound and lower bound?

A MACD is a difference between two moving averages, typically, 12-day Exponential Moving Average and 26-day Exponential Moving Average. With some stock prices, I observed that the range of there MACD ...
0
votes
2answers
43 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 ...
0
votes
1answer
29 views

Probability question help

A company that sells annuities must base the annual payout on the distribution of the length of life of the participants in the plan. Suppose the distribution of male participants' lifetimes is ...
0
votes
1answer
92 views

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need?

I have a mean and a desired range for a normal distribution, how do I discover what standard deviation I need? I may not be using the correct terminology so here's a graph: Based on this, if you ...
2
votes
1answer
66 views

Estimate the true mean: given only measurements above a known threshold

I have a computer-generated logfile which shows events which took longer than a particular time threshold (say 1 second for the sake of argument): if I measure the mean of these measurements, it seems ...
0
votes
0answers
17 views

is f-mean a general form for all well-behaved means?

Can one claim that all well-behaved means can be written in form of f-mean? I mean means like logarithmic, etc. wikipedia link
0
votes
1answer
236 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
61 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 ...
0
votes
0answers
48 views

About a special way to find the average waiting time to get a sequence

A friend of mine taught me the following question: You have a coin. When you toss it up, heads you note $1$, tails you note $0$. Then, tossing it up repeatedly, let's find the average waiting time to ...
1
vote
2answers
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} ...
2
votes
3answers
65 views

Why should ${\sum_1^n {s_i} \over \sum_1^n {t_i}} = {n \over \sum_1^n{t_i \over s_i}}$? (harmonic mean)

I realized it reading about computer performance. This identity is presented there with words: dividing total distance by total time, you arrive at average execution rate on the left. On the right, ...
0
votes
2answers
68 views

Bringing numbers in a set closer together

I'm trying to express the relative scale of items compared to an "average" scale for all items in the set. This produces values like { 0.5, 1.8, 0.3, 1.2 ... } I then wish to use this number to ...
1
vote
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.
0
votes
1answer
34 views

Average amount needed for x number of months remaining

I'm trying to calculate the average amount of profit needed to hit a milestone based on the number of months remaining. So let's say the goal is £1,000 and there are 5 months left. If I have £400 ...
2
votes
0answers
58 views

The angle of an average rotation is $126.5^\circ$?

In the paper "Applications of Quaternions to Computation with Rotations" by Eugene Salamin, 1979 (click here), they get 126.5 degrees as the mean value of the rotation angle of a random rotation (by ...
1
vote
1answer
387 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 ...
1
vote
2answers
586 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 ...
0
votes
2answers
136 views

Calculate the average sales per day in 2010.

In 2005, Company K was 730 000 units of the car market. Total sales is 50% of the total cars sold in 2010. Calculate the average sales per day in 2010. Calculation: 1) 50/100 x 730 000 2) 730 000 x ...
-1
votes
2answers
66 views

What is the calculation for an average speed? [closed]

George is driving 100 miles in 1 hour and 30 minutes. What is the calculation involved when looking for an average speed of George? Answer: Divide 100 by 1.5 How to make the calculation for the ...
5
votes
1answer
132 views

continuously averaging a stream of numbers

Ok, so I'd like a little help with the mathematical theory behind something I'm doing in a program. I've got a stream of numeric inputs, and I need to find the average of all the numbers in this ...
28
votes
2answers
2k views

What's the mean of all real numbers?

At first, I had thought the average must be zero, since for every positive number there's an equal magnitude negative number to cancel out the positive number's effect on the average, leaving only ...
0
votes
1answer
107 views

average/weighted average within Excel

5 star 128 4 star 17 3 star 10 2 star 2 1 star 14 Average stars 4.42 How many more 5 stars would I need to get ...
1
vote
0answers
61 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 ...
8
votes
5answers
358 views

Puzzle in Percentages

Okay, this is a real-time problem. The following is a picture of Customer satisfaction rating, which was displayed next to an item in an online shopping website. Satisfied customers click the ...
0
votes
1answer
73 views

different types of Averages : prove there is an inequality between different averages

This is something I have been curious based on observations I have made by analyzing data from the energy industry. The context is you have monthly data for energy used per month and the cost per ...
3
votes
2answers
185 views

If I put $M$ balls into $N$ boxes at random, what is the average number of balls in the boxes that are not empty?

I have a very brief question: if I put $M$ balls into $N$ boxes at random, what is the average number of balls in the boxes that are not empty?
2
votes
3answers
62 views

What is the mean score for the $20$ rolls?

A fair die is rolled twenty times. The results are shown in the bar graph. What is the mean score for the $20$ rolls?
2
votes
2answers
382 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 ...
1
vote
2answers
53 views

Problem Solving using Algebra

If Peter is $7$ years older than Sharon and John is twice as old as Peter, work out how old Peter is if the average of their ages is $19$. Thanks! :)
0
votes
1answer
58 views

Find the value of each number which derives an average given a starting point, end point and total of numbers used.

Given an average, a low number, a high number and the total amount of numbers used (stated) to derive the average, is there a formula to determine what the value of each number was, that amounted to ...
3
votes
1answer
62 views

Is it always true that “max $\ge$ average + sigma”?

Assume that $i$ from $1,\ldots,N$, $x_i \ge 0$ and: $$\mathrm{avg} = \frac{\sum_i x_i}{N}$$ $$\sigma = \sqrt\frac{\sum_i{(x_i-\mathrm{avg})^2}}{N}$$ Is that true that: $$\max_i x_i \ge ...
1
vote
1answer
157 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 ...
0
votes
1answer
36 views

Calculate the new average using standard deviation?

This is for a programming exercise. I have: the last average value the last standard deviation the total number of values I need to be able to add a new value to my average without knowing the ...
1
vote
1answer
598 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 ...
1
vote
1answer
33 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 ...
0
votes
2answers
58 views

Quadratic and geometric average

I'd like to find the find the quadratic average and the geometric average. To do this I have these informations : The standart deviation, the arithmetic average and the number of values. I know the ...
1
vote
1answer
89 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 ...
0
votes
2answers
63 views

Is there another name for power mean, where p=1/2

What would you call this type of average? $\left(\frac{1}{n} \sum_{i=1}^n \sqrt x_i \right) ^ 2$
1
vote
4answers
336 views

Finding mean of $n$ consecutive numbers using a shortcut

I am working on the following question: Let us say we have $n$ consecutive numbers labelled $x_1$ to $x_n$. I want to find the average of these. The quickest way to do this seems to be ...
0
votes
1answer
62 views

How to calculate avaerage of the average

I am having data of 10 schools, each school is having different no of sections. Each section students attended different no of computer classes. How to calculate the average no of computer classes ...
0
votes
1answer
222 views

Find out Average and Percentile from the Histogram

Below is my Histogram information- {178=18, 213=1, 114=76, 139=5, 131=10, 176=13, 95=229, 1444=1, 206=5, 192=4, 227=2, 185=12, 67=14, 199=4, 148=11, 124=21, 75=226, 1431=1, 123=29, 157=16, ...
1
vote
1answer
48 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 ...
1
vote
1answer
371 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}) = ...