# Tagged Questions

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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### Maximise difference between mean and median

I have a set of numbers and I want to maximise the difference between the mean and the median by removing a given number of elements. For instance I have the following set: ...
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### Average $y$ from a range of $x$ in a parabola

Given a parabolic/quadratic formula such as $ax^2 + bx + c =y$, how do I get the average value of $y$ given a range of $x$ ($x_{min}$ to $x_{max}$). Real world example: if my formula represents the ...
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### How do I properly average these percentages?

I have attendance records for an annual event: person 1: $4$ of $8$ attended $= 50.00$%, or every $2$ years person 2: $1$ of $4$ attended $= 25.00$%, or every $4$ years ...
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### Calculating the average speed of a trip when given 3 different speeds for 3 percentages of distances.

The question: In a trip, $10$% of the way, Lucy drives uphill at an average speed of $56$mph; $10$% of the distance is downhill where she can manage an average speed of $72$mph. On flat ground, Lucy ...
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### What star rating is representative of this distribution? [on hold]

100 people vote. They can vote 1, 2, 3, or 4 stars. Distribution: 1 = 33, 2 = 26, 3 = 12, and 4 = 28. What star rating would you say is "representative" of these 100 people: 2.36 (2), the average, ...
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### Average number of $5$-card draws before all $52$ cards in a deck are drawn.

So an interesting question was brought to me today and I'm not sure how to formulate the equation to answer it. A person draws $5$ cards from a deck, writes the cards down, puts the cards back in the ...
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### Approximate values from point groupings

Say I am given a set of values: \begin{bmatrix}0.9&1.1&1&1.95&2&2.05&2.95&2.95&3.1&3\end{bmatrix} Is there a way I can get the 'center' or 'average' values 1, 2, ...
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### Multiple server queuing model

I have come across the following problem in one of my courses: Let's suppose a patient in a hospital is waiting to be picked by one of the two doctors available. The time till a new pacient arrives ...
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### Using double integration to compute an average yields a different result than computing it without integration

I'm self-learning multivariable calculus and am using double integration to compute the average value of $f(x,y)$ over some region. I'm trying to solve the following simple problem using two different ...
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### Generalizing exponential moving average to n samples

Assume that we have a moving average like this: $E_t = a*S_{t-1}+(1-a)*E_{t-1}$ where $E$ would be an estimate we are interested in, and $S$ is a sample we take at each point in time. Now, if we ...
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### Find the percent of boys and girls

I have a basic school academic question which despite of trying very hard I was unable to find a solution - Average score of girls is an exam is $67$ and that of boys is $62$. Find the percentage of ...
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### Number of Likes and Dislikes to Star Rating system

I have a 5 star rating system that outputs a recommendation. A user inputs a rating based on a Like or Dislike. What I would like to know is how to convert the number of likes and dislikes into a ...