Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [median]

The median is the value below which half the data or probability distribution lies - when the sample size is odd, the median is the 'middle' value of an ordered sample.

The median is the value above which, and below which, half the data lies. If the number of data is odd, the median is the middle value when the sample is ordered; if the number of data is even, the median is the mean of the two middle values when the sample is ordered.

  • The median can be considered an appropriate measure of central tendency for an ordinal level variable.
  • It is often considered a more representative measure than the mean, even for interval data, when the distribution is highly skewed.
  • Medians are more robust (but less efficient) measure when the data may be contaminated.
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Median of Medians calculation

I do a bunch of real estate reporting and the median price is often reported, particularly by the NAR (National Association Of Realtors). As best I can tell, they only get the medians of real estate prices from each area. My question is, how should…
dartdog
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Median value on ordinal scales

I have been reading about appropriate measures of central tendency for ordinal level data. So far I have learned that the median and mode can be used but that the latter can only be used in some cases. Some sources state that the median can only be…
Anne
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Relation between Pi and the Median

I was reading about efficiency here and came across something curious. For large N the sample median is approximately normally distributed as Then again here I found that for a sample of size N=2n+1 from the normal distribution, the efficiency…
Sumner18
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How can I prove that the median is a nonlinear function?

My question flows out of the top answer to this question, from which I learned that a "linear function" is any function $f$ with properties of additivity and homogeneity of degree 1: $$ f(x + y) = f(x) + f(y) \\ f(ax) = af(x) $$ Just reflecting on…
user1205901 - Слава Україні
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What is the median of the school grades A A B B ?

If the sample was $S_1=\{1,2,3,4\} \subset \mathbb R $ the median is 2.5 because 50% of the sample is $>=$ 2.5 and 50% of the sample is $<=$ 2.5. The median obviously does not need to be element of the sample, since 2.5 $\notin S_1$. Assume the…
HOSS_JFL
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Extension of Median to big data integer distributions?

I am analysing big samples of integer values. Because they come from a non-symmetrical distribution (high positive skew), I prefer to use the median to characterise central tendency, not the mean. However, due to the nature of the data, many values…
Mark Shovman
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Software for median polishing

Is there any easy-to-use software for Tukey median-polishing rows and columns with lots of missing values?
user42520
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How to calculate the median age of a population?

I want to calculate the median age of a population. Consider the following example data (downloaded from Statistics Canada's CANSIM database, Table 051-0001): Table 051-0001 Estimates of population, by age group and sex for July 1, Canada, provinces…
Werner
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Existence of a Smoothed Median Function

The median of a finite set of data depends on the data in a continuous, but non-smooth way; this can be demonstrated by considering the median of the data set $\{ 0, 1, x \}$ as $x$ varies. I wanted to know whether people have derived median-like…
πr8
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Calculating Median Speed with Spotty Data

I have a situation where I need to calculate the speed of a vehicle for a given time period. The data I'm working with is very spotty in the temporal dimension— we might have 5-10 speeds recorded within seconds of each other, but other speeds in the…
Jim Heising
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How do I emphasize a speed increase between two sets of data?

I've run a test on a program, upgraded the program and then run the same tests again. The first test showed that the median time for the program to respond was approximately 2.0 seconds. The second test showed that, after the upgrade, the median…
GamerJosh
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What is the equivalent of the SEM for the median?

I can calculate the standard error of the mean as: $SEM=\frac{\sigma }{\sqrt{n}}$ where $\sigma$ is the standard deviation and $n$ the sample size. I would imagine that the equivalent for the median is simply: $SEMedian=\frac{MAD}{\sqrt{n}}$ where…
francoiskroll
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How to calculate median via interpolation

I am reading a text on data mining. I came across this formula, but I do not understand how to apply it. There aren't any examples following the forumla and my research online has produced very few results. Can someone explain how to apply this…
Evan Gertis
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What is the difference between a median and a population/sample median?

If I have an order statistic, I can rank them from smallest to largest like $$X_{(1)}, X_{(2)},...,X_{(n)}$$ and there will be some median $X_{m}$. But I can also have some distribution $f(x)$ and define an integral $$\int_{0}^m f(x)dx =…
Stan Shunpike
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Effectiveness of Median

New to this board and hoping this question is something easy to describe. I am working on a project that look at median cycle times of emergency department patients length of stay. Across a quarter, the sample size is fairly large (n=5000). …
Eric B
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