The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.
22
votes
11answers
4k views
Prove that if two miles are run in 7:59 then one mile MUST be run under 4:00.
I'm in an argument with someone who claims that a two mile in 7:59 does not imply that one mile (at some point within the two miles) was covered in under 4:00. This is obviously wrong, but I'm not ...
20
votes
4answers
820 views
What is to geometric mean as integration is to arithmetic mean?
The arithmetic mean of $y_i ... y_n$ is: $$\frac{1}{n}\sum_{i=1}^n~y_i $$
For a smooth function $f(x)$, we can find the arithmetic mean of $f(x)$ from $x_0$ to $x_1$ by taking $n$ samples and using ...
8
votes
4answers
1k views
How do I figure out what kind of distribution this is?
i've sampled a real world process, network ping times. The "round-trip-time" is measured in milliseconds. Results are plotted in a histogram:
Ping times have a minimum value, but a long upper tail.
...
7
votes
3answers
244 views
Asymptotic difference between a function and its binomial average
The origin of this question is the identity
$$\sum_{k=0}^n \binom{n}{k} H_k = 2^n \left(H_n - \sum_{k=1}^n \frac{1}{k 2^k}\right),$$
where $H_n$ is the $n$th harmonic number.
Dividing by $2^n$, we ...
6
votes
4answers
100 views
Is there a way to get an average that weights each item inversely based on distance from the mean?
I'm not sure how to phrase this, or even if such a thing exists. Sorry!
I have a bunch of data points, which are mostly pretty tight. Each group should hone in on a specific point in space. ...
6
votes
1answer
2k views
Average percent increase not equal to total percent increase?
I tried searching around for this but it was difficult to boil down the search terms. Plus nothing seemed to be showing up anyway.
What's an easy way to show that the average percentage increase of n ...
5
votes
4answers
764 views
How can I calculate “most popular” more accurately?
I'm developing a website at the moment.
The website allows users to "rate" a post from 0 to 5.
Posts can then be displayed in order of popularity.
At the moment, my method of calculation is pretty ...
5
votes
4answers
316 views
Average bus waiting time
My friends and I were "thinking" yesterday in the pub about the following: if a person is standing on a bus stop that is served by a single bus which comes every p minutes, we would expect the average ...
5
votes
1answer
758 views
Incremental averageing
Is there a way to incrementally calculate (or estimate) the average of a vector (a set of numbers) without knowing their count in advance?
For example you have ...
5
votes
1answer
561 views
Calculate average latitude / longitude
I have the array of geographical coordinates (latitude & longitude).
What is the best way to calculate average latitude and longitude?
Thanks!
5
votes
1answer
336 views
Harmonic mean and logarithmic mean
The harmonic mean of a finite set of positive real numbers $\{x_1, x_2, \ldots, x_n\}$ is defined to be $$H(\{x_1, x_2, \ldots, x_n\}) = \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + ...
5
votes
3answers
1k views
Which average to use? (RMS vs. AM vs. GM vs. HM)
The generalized mean (power mean) with exponent $p$ of $n$ numbers $x_1, x_2, \ldots, x_n$ is defined as
$$ \bar x = (\frac{1}{n} \sum x_i^p)^{1/p}. $$
This is equivalent to the harmonic mean, ...
5
votes
2answers
310 views
How many decimal places are needed for incremental average calculation?
If using the following formula to incrementally calculate average value:
$$m_n = m_{n-1} + \frac{a_{n}-m_{n-1}}{n}$$
And the number of decimal places to where you can save $m_n$ is limited to $d$ ...
4
votes
1answer
202 views
Prove that if 2000 m is run in 4:50, then one mile is run under 4:00
Prove that if 2000 m is run in 4:50, then one continuous mile is run under 4:00.
I was thinking -- yeah, this follows easily from the other question, where I asked that if 2 miles are run in ...
4
votes
2answers
116 views
Basic question about natural density
Suppose that we have a sequence of finite sets $A_1, A_2, \ldots$, which partition $\mathbb{N}$. I am making no other assumptions on the $A_n$ - i.e. there could be any amount of interleaving between ...
4
votes
5answers
150 views
what is the argument for not using the average of an average?
I want to disprove someone's calculation of percentage of cash sales for a year by taking summing percentage of cash sales by month and dividing by 12. I sense the correct way is to take total cash ...
4
votes
2answers
582 views
Why is median age a better statistic than mean age?
If you look at Wolfram Alpha
or this Wikipedia page List of countries by median age
Clearly median seems to be the statistic of choice when it comes to ages.
I am not able to explain to myself ...
4
votes
1answer
206 views
Regular average calculated accumulatively
is it possible to calculate the regular average of a sequence of numbers when i dont know everything of the sequence, but just everytime i get a new number i know the total count of numbers and the ...
4
votes
2answers
3k views
Why is an average of an average usually incorrect?
Can someone explain why taking an average of an average usually results in a wrong answer? Is there ever a case where the average of the average can be used correctly?
As an example, let's say ...
4
votes
1answer
205 views
How to calculate an overall 5 star rating based on other weighted 5 star ratings
I have these 3 ratings. I want to combine them to produce an overall rating out of 5. The overall rating can be a float, so no rounding is necessary, but it cannot be negative. I'm just not sure ...
4
votes
4answers
7k views
Sum of averages vs average of sums
I have essentially a table of numbers -- a time series of measurements. Each row in the table has 5 values for the 5 different categories, and a sum row for the total of all categories.
If I take ...
4
votes
1answer
155 views
Average over angles
I feel quite dumb for asking this, but it's getting a bit frustrating.
I have a function which depends on $\theta$ and $\phi$ in spherical coordinates:
$$ f(\theta, \phi) = \sin^2 \theta ...
4
votes
2answers
117 views
Is there a name (and use) for an average based on the unique values of a set of data?
Consider the following data points: 1, 1, 2, 3, 4
I understand that...
the average is the total of the numbers divided by the count of numbers in the set, the median is the central value based on ...
4
votes
1answer
151 views
Power Mean Random Distribution
I'm trying to find a the distribution for the power mean of $n$ random variables on $[0,1]$.
I've got the arithmetic mean: $\frac{n}{(n-1)!}\sum_{k=0}^{\lfloor ...
4
votes
2answers
510 views
Real world examples for Mode in Statistics
I am looking for some real world examples for mode in Statistics involving topics which students like say Football or Social networks. Also they need to clearly identify differences in the usefulness ...
4
votes
1answer
101 views
Probability value in a skewed data
A question goes like this:
Given that there 2 questions out of 3 questions to pass an exam and follow are details of number of people who attended the questions correctly, what is the maximum number ...
3
votes
1answer
2k views
5 star ratings. Bayesian or Weighted average?
I am building a website which has 5 star ratings to rate items.
These ratings unlike the normal ones are of unequal weights. i.e.
...
3
votes
4answers
174 views
If $\sum\limits_{k=1}^n y_k\geq n$ and $\sum\limits_{k=1}^n \frac{1}{y_k}\geq n$, then $\prod\limits_{k=1}^n y_k\geq 1$?
Let $y_1,\ldots y_n$ be positive real numbers satisfying
$y_1+\cdots+y_n\geq n$ and $\displaystyle{\frac{1}{y_1}+\cdots+\frac{1}{y_n}\geq n}$.
Is it true that $y_1y_2\cdots y_n\geq 1$?
3
votes
3answers
160 views
Erased number?
A set of consecutive positive integers starting with 1 is written on the board. A student came along and erased one number. Average of remaining numbers is 61 15/20 . What was the number erased
3
votes
2answers
799 views
Find the average of a collection of points (in 2D space)
I'm a bit rusty on my math, so please forgive me if my terminology is wrong or I'm overlooking extending a simple formula to solve the problem.
I have a collection of points in 2D space (x, y ...
3
votes
3answers
211 views
Definition of random
Suppose that you has to guess given a set of numbers
If they are random.
The mathematical expectation
Is there a definition of randomness that allow this prove/test?
Is even possible? if so: How ...
3
votes
2answers
342 views
Average Distance Between Random Points in a Rectangle
My question is similar to this one but for rectangles instead of lines.
Suppose I have a rectangle with sides of length $L_w$ and $L_h$. What is the average distance between two uniformly-distributed ...
3
votes
2answers
317 views
APR Calculation
I'm hoping someone can clarify this for me.
The model/example is this:
We lend an amount of 1498.50 (loan amount). Other fees total 39.95.
The term of the loan is for 12 months. There is no ...
3
votes
1answer
31 views
How do I average a new number into an established percentage if I know the number of items?
This seems like something I should be able to do but I can not for the life of me figure it out. I'm writing a program to calculate an average score; let's say that my data looks like this.
x = ...
3
votes
2answers
151 views
Course Grade - Statistics Question
I'm confused about finding the standard deviation of various weighted objects in a problem. For example, consider an academic setting, with four assessments as follows:
...
3
votes
1answer
757 views
leading and lagging moving average indicator
What are leading short and lagging long moving average indicators and how do we calculate them?
e.g. for the following data set, and let window size be 2. Can you ...
3
votes
1answer
207 views
Average sine of an angle between two rays in a cone
I'm looking for an average value of sine of an angle between two rays, lying within a cone with a certain angle.
Given a cone with an aperture of ${2\chi}$ and two rays lying within the cone. The ...
3
votes
2answers
396 views
What do curly brackets mean in this formula?
In this paper, in the Formula at the beginning of 2.2, we have
$B=\{b_i(O_t)\}$
where
$i=0,1$ - the number of probability formula
$O_t$ - the state at moment $t$
$b_i(O_t)$ - two probabilities ...
2
votes
3answers
78 views
Problem with calculating average.
I came across the following question.
A man travels a distance of $20$ miles at $60$ miles/hr and then return over the same route at $40$ miles/hr. What is the average rate for the round trip in ...
2
votes
3answers
172 views
Average amount of money received from pulling three random coins
Let's say I have a bag of coins, which contains 1 quarter, 2 dimes, 3 nickles and 4 pennies. If I were to randomly pull out 3 coins, on average, how much money would I get?
2
votes
2answers
338 views
What is the average of rolling two dice and only taking the value of the higher dice roll?
What is the average result of rolling two dice, and only taking the value of the higher dice roll?
To make sure the situation I am asking about is clear, here is an example:
I roll two dice and one ...
2
votes
3answers
147 views
Averaging the values of $\cos x$ over one period
I'm calculating the average value of $\cos x$ by dividing the period $[0,2\pi]$ into ten intervals which means that I should be looking for the average of 11 results. What I get is approx. 0.09. The ...
2
votes
1answer
367 views
Need help with a math trick question
I wasnt sure where to ask this but since this is an algorithmic question here it goes. I've come face to face with a math problem and can't seem to get over it for the last couple of days. It goes ...
2
votes
1answer
47 views
What is this physics simulation formula doing?
I have encountered a piece of code that performs a physics simulation of a moving projectile. I'm trying to understand what the mathematical basis is for a bit that looks like this:
$$
d_1 = f(x)
$$
...
2
votes
2answers
60 views
Calculating statistic for multiple runs
I have s imple, general question regarding calculating statistic for N runs of the same experiment. Suppose I would like to calculate mean of values returned by some Test. Each run of the test ...
2
votes
2answers
748 views
Finding percentile rank without knowledge of distribution
Say you take a test and are told your individual score, as a percentage. Eg: 95%.
You are also told the aggregate score (average) of all students together, as well as how many students in total took ...
2
votes
2answers
103 views
Probability cut-off
Is there a probability cut-off point?
e.g. if the probability of something keeps halving do you stop at a certain point and say the rest of the possibilities are negligible?
What do you do then?
...
2
votes
2answers
266 views
How do I average out to a particular number if I have to add another number to get that average?
So, lets say, that you have the following numbers (4, 15, 3, 22) and you have to add the fifth number (which I would call X) and they must average out to say 20.
What do you have to do?
I figured ...
2
votes
2answers
543 views
Average distance between two points in a circular disk
How can I find an average distance between two points lying inside a circular disk of a certain radius?
I wonder if there is any other way except of using a Monte Carlo method?
2
votes
1answer
76 views
What is the best way to average the frequency of Chinese characters in a sentence?
I'm trying to find the best way to assign a "frequency score" to sentences in Chinese. Basically, I have a database which tells me how frequent each Chinese character is. From that, I would like to ...
