# 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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### 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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### Is it possible to find Median of set contains string value as well as Null value?

I am doing one calculation on Median and AFSIK about Median, it can be calculated by a "set of Finite set of Numbers". Now if a set has following value as: A = {3,4.56, 2, 11, JAMES, , Joy, 54, 9} ...
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### Median of waiting time for $k$-th ace from bridge cards

I can't figure out how to get median of a waiting time from the exercise 36 from W. Feller's book An Introduction to Probability Theory and Its Applications Vol.1 (bold in the quote): ...
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### Does the median tend to the lower limit of the median class?

The median for a continous distribution is given by $M= L +\dfrac{(N/2-C)\cdot I}{f}$ where $M$ is median, $L$ is lower limit of median class, $N$ is the total frequency, $C$ is the cumulative ...
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### Ordering of positive integers

Three positive integers: m. n and q, their average is 10, median is m+6. what is the greatest possible value of Q ? I understand how to find the solution which I am outlying below. My question is ...
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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 $b$, ...
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### Prove the median of a uniform distributions is $\frac{1}{2}(a+b)$

Let X~U(a,b) with a and b in the real line, such that b>a with X's pdf given by $$f_X(x)=\frac{1}{b-a}\mathbb{1}(a<x< b)$$ Show the median of X's distribution is given by $$m=\frac{1}{2}(b+a)$$ ...
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### How to understand the Repeated Median Estimator (Siegel 1982)?

I guess I did not understand the formula of the repeated median estimator introduced by Siegel (1982): This is the formula: If I got the following time series for instance: ...
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### 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 ...
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### 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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### Means and Median of Probability

The question is: pennies come in rolls of 50. Out of the 200 rolls a bank is storing, 12 have all Canadian pennies: the remaining 188 rolls contain at least one American penny. In the 200 rolls, about ...
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### Prove That The Composite Median Of Two Groups Lies Between Separate Medians of The Groups

Let $M_1$ be the median of $n_1$ observations and $M_2$ be the median of $n_2$ observations. Show that $M$, the median of$(n_1+n_2)$ observations combined, lies within $M_1$ and $M_2$.
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### Is this the correct way of calculating the median?

I just completed the June $2009$ mei stats paper. On the mark scheme for question $5ii$ it shows the median being calculated using $600$, shouldn't it be $600+1$? I thought the median was calculated ...
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### Determination of the lengths of the medians of a triangle.

The lengths of the sides $AB, BC$ and $CA$ of a $\triangle ABC$ are respectively $√14, √26$ and $√56$. What are the lengths of the medians of the triangle?
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### Multiple, One (?), or No Medians for discrete

I am a bit confused on how medians are calculated for discrete distributions. I understand that there can be multiple medians or none at all. Can there be one median for a discrete distribution? Can ...
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### calculation of median of grouped data

While calculating the median of grouped data of total frequency $N$, in order to find the median class which value should be taken into consideration to match against cumulative frequency : $\frac N2$ ...
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### Should I use interpolation when finding median, and quartiles?

I am a S1 maths (Edexcel) AS student in the UK. My question: Say we have a stem-and-leaf diagram with 26 values. We want to find the lower quartile. To get the marks for our specification, we need to ...
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### The validity of dividing an average cost by an average duration?

Let's say you wanted to calculate, for example, the average (i.e. mean) cost per day for a hotel to accommodate a tourist. If only aggregate cost data is available, is dividing the average cumulative ...
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### Can you further explain or clarify the proof of this?

I am trying to prove that $AG = 2(GD)$, given $AD, BE$ and $CF$ are 3 medians meeting at point $G$ of a triangle $ABC$. I found this website that seems to show what I want to prove: http://jwilson.coe....
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### Another name for mode frequency

Is there another term for the number of times the mode number occurs in a list/array of numbers or 'the frequency of the mode' in a list/array of numbers? Apologies if this has been asked before - I ...
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### Median of the sample median equal to the median of the distribution?

I'm taking a course in mathematical statistics this semester. I don't know how much consensus there is among mathematicians about notations and definitions, so I'll just define the essentials. Let me ...
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