The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.
0
votes
1answer
997 views
How do I calculate weighted mean with negative weights?
This might be very trivial for you guys.
If :
I buy 2 oranges for 5 dollars each then
I buy 3 oranges for 6 dollars each and then
I sell 3 oranges for 4 dollars each
How do I calculate the average ...
3
votes
1answer
759 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 ...
0
votes
1answer
111 views
I'm having trouble calculating ratings
I'm not a wiz at math and this problem has me a little stumped. I need the average score out of 5 but it's a little different how I do it.
I have 5 fields, field one is rating one, field two is ...
2
votes
2answers
174 views
How can I show this in a summation?
I am trying to work out a summation for packet delays which is very similar to the summation for estimating RTT, which is an exponentially weighted moving average. I have modified the estimating RTT ...
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 ...
1
vote
1answer
1k views
Proving correlation coefficient = 1 or -1 given X and Y=a + bX
Given $X$ and $Y = a+bX$, I have to prove that:
If $b \lt 0$, then $\rho = -1$. If $b \gt 0$, then $\rho = 1$.
I've gotten to the point where I have:
$$ \rho = \frac{b \cdot \sigma_x }{ ...
3
votes
2answers
800 views
Find the average of a collection of points (in 2D space)
I'm a bit rusty on my math, so please forgive me if my terminology is wrong or I'm overlooking extending a simple formula to solve the problem.
I have a collection of points in 2D space (x, y ...
0
votes
1answer
725 views
How to add and subtract values from an average?
Say I have 100 numbers that are averaged:
number of values = 100
total sum of values = 2000
mean = 2000 / 100 => 20
If I want to add a value and find out the ...
1
vote
1answer
156 views
Bound on deviation between arithmetic and harmonic mean?
It is well known that, if HM denotes the harmonic mean and AM the arithmetic mean, we have
$$ AM(x) \ge HM(x) $$
Now I am dealing with the expression
$$ \frac{1}{HM(x)} - \frac{1}{AM(x)} $$
A ...
20
votes
4answers
820 views
What is to geometric mean as integration is to arithmetic mean?
The arithmetic mean of $y_i ... y_n$ is: $$\frac{1}{n}\sum_{i=1}^n~y_i $$
For a smooth function $f(x)$, we can find the arithmetic mean of $f(x)$ from $x_0$ to $x_1$ by taking $n$ samples and using ...
4
votes
1answer
101 views
Probability value in a skewed data
A question goes like this:
Given that there 2 questions out of 3 questions to pass an exam and follow are details of number of people who attended the questions correctly, what is the maximum number ...
5
votes
1answer
336 views
Harmonic mean and logarithmic mean
The harmonic mean of a finite set of positive real numbers $\{x_1, x_2, \ldots, x_n\}$ is defined to be $$H(\{x_1, x_2, \ldots, x_n\}) = \frac{n}{\frac{1}{x_1} + \frac{1}{x_2} + \cdots + ...
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 ...
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
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 ...
4
votes
2answers
585 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
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 ...
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.
...
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, ...
