# Tagged Questions

For questions about the numerical value separating the higher half of a data sample, a population, or a probability distribution, from the lower half.

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### How to calculate the median when each value from the data is increased by 10?

Given that a collection of scores on a quiz leads to a mean of 40, a median of 38, and a mode of 36. If we added 10 points to each score what would be the new median?
4k views

### How do I find percentiles of data sets (Even vs odd)?

Given the following data set with an even number of values: $100, 100, 105, 113, 129, 132, 146, 152, 176, 200$ The value representing the 30th percentile, using the formula n(p/100) where n = sample ...
7k views

### The median minimizes the sum of absolute deviations

Suppose we have a set $S$ of real numbers. Show that $$\sum_{s\in S}|s-x|$$ is minimal if $x$ is equal to the median. This is a sample exam question of one of the exams that I need to take and ...
21 views

### Median poker hand (Texas Hold’em)

I try to find the median poker hand (Texas Hold’em). The following is given: 1) There are 52 cards 2) Assuming seven of them are chosen randomly 3) Create the best possibility with 5 of these 7 ...
117 views

### The problem of congruent areas in a triangle.

A problem was posed in front of me and I couldn't solve it after multiple attempts-- Consider any triangle and 3 concurent cevians are drawn from each of its 3 points . Now the figure formed has 6 ...
31 views

### box and whiskers plot

I am having some troubles understanding what the components of a box and whiskers plot mean. Let's say I have some observations. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ...
723 views

### Given x is an exponential random variable, find median & probability

For the median, I believe that I should integrate the function, ∫x0λe−λtdt=1−e−λx Then I need 1−e−λm=.5 for m, which is equivalent to e−λm=.5. m=ln(2)/λ =>m=ln(2)/.2
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### Probability of $n$ numbers picked from set to have greater mean than set

If we have (N) varying non-negative numbers , with a mean equal to X, and a median less than X, if we pick (n) unique numbers from the set, what is the formula for the probability that the mean of ...
21 views

### Formula for the weighted median

I am looking for mathematical notation (not computer code) for the following simple scenario: I have three numbers: 6, 7 and 2. I wish to find the weighted median where the weights are say, 20, 10, ...
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### Statistics. How to find the median of two other medians?

I got median of 226 and another median of 304. Now the question is how to find the overall median? Averaging them is not the correct answer.
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### Geometric median (or Fertmat-Webber problem), including continuous case

For a finite set $X\subset \mathbb R^n$ the geometric median is defined as the point in $\mathbb R^n$ for which the sum of distances to all points of $X$ attains its minimum. Here is a wiki article: ...
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### Area of triangle constructed from the medians of other triangle

We have triangle ABC of area P. Is it possible to compute the area of a triangle with sides "made" from medians of the triangle ABC in terms of P I'm looking for some hints maybe,
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### non-linearity of median - proof

I'd like to show counterexamples for: a. $med(X+Y) = med(X) + med(Y)$ b. $med(aX+b) = a\cdot med(X) + b$. Showing that "a" is not correct: Let $X, Y$ be independent random variables with ...
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### Relationship between subset medians and the median

Suppose we have a set of data $A = \{a_1, a_2, \dots, a_n\}$ and $B = \{b_1, b_2, \dots, b_n \}$. So there are $2n$ elements in total. Further suppose the median of $A$ and $B$ is $a$ and $b$, ...
Problem: A pharmacy has a uniform annual demand for 200 bottles of a certain antibiotic. It costs \$10 per year for a storage place for one bottle, and$40 to place an order. How many times during ...