# Tagged Questions

The sum of several numbers divided by their count nicely summarizes the overall size of the numbers involved in a single value.

382 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. ...
4k 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 ...
134 views

62 views

### Derivation of Running(Online) Variance's formula

I need to know the dimostration of Running Variance's formula: $$\sigma_n^2 =\frac{(n-1)\sigma_{n-1}^{2}+(x_n-\overline{x}_{n-1})\cdot(x_n-\overline{x}_{n})}{n}$$
355 views

### Remove statistical outliers

I've analysed newspapers by counting the language distributions of the articles. The results look like that: ...
1k 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?
79 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 ...
381 views

### How to establish this inequality: $(1-a)(1-b)(1-c) \geq 8abc$ for $a+b+c=1$?

Let $a$, $b$, and $c$ be positive real numbers such that $a+b+c = 1$. Then how to establish the following inequality? $$(1-a)(1-b)(1-c) \geq 8abc.$$ My effort: Since $a+b+c =1$, we can write  (...
470 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 ...
3k views

### Use calculus to calculate the slope of a moving average line

I recently read a paper where it was stated that calculus was used to calculate the slope of a moving average line at a given point. Given that there is no real formula to differentiate with a moving ...
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! :)