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.

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Distribution of median and median absolute deviation

what is the distribution of median and median absolute deviation for sample from normally distribution function? 2. Since the distribution of variance follow a chi square distribution with n-1 degree ...
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Meta-analysis: Estimating the population median

The Borenstein (2008) textbook I'm using doesn't make any references to estimating a population median. Searching the internet I find lots of references to using the median and range to estimate the ...
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27 views

median proof given G(t)=F(t-delta) [closed]

How can I do part a? I get stuck after using the formula for difference of 2 independent variable
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CLT and Wald-Wolfowitz runs test asymptotic distribution

I need help finding a theorem which could be used to prove that the Wald-Wolfowitz runs test is asymptotically normal. Let me formalize my question. We have a random sample $\{X_0,X_1,...,X_n\}$ (if ...
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Convergence to zero of a sum involving the median

Can anyone help me with this? Let $\{X_i:i=1,...,n\}$ be a sequence of i.i.d random variables with a continuous density function. If $m$ is the true median and $\hat m _n$ is the sample median, is it ...
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71 views

Maximum of a set of values from given mean and median

The arithmetic mean and median of $5$ distinct natural numbers are both $7$,what may be the maximum of the $5$ numbers? Here we see that the median is the $3rd$ value.Also the sum of the numbers is $...
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Is there a statistically significant difference between two methods, which test should I use & am I violating random assumption?

I collected data for every 2016 Republican primary that has available at least 3 polls, according to the polling data aggregated by RealClearPolitics.com. In a spreadsheet for each row which indicates ...
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Higher variance in sample mean or sample median? [duplicate]

The variance of the sample median depends on the distribution you are sampling from. This is also true for the variance of the mean. But can one say that the variance of the sample mean is always ...
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error propagation on the median

Suppose to have a set of exact data $x_i, i=1,\dots,N$ and to calculate its median value $m$. Then, a sound way to estimate the error $\delta m$ on $m$ would be bootstrapping. (I think...) But what ...
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Robust statistic for representing small dataset with outliers and representing them graphically

I'm evaluating different systems varying a certain parameter common to all of them. Let this parameter be x. At each x value I ...
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34 views

mean\medians as data points in two way repeated measures ANOVA

I have a table with 12 columns each regarding one combination of three (2X2X3) diffrent conditions in an experiment. Each row (25) represent a subject that did the experiment. Each data point in the ...
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562 views

Is there a formula for computing median?

Is there an equivalent of the mean formula: \begin{equation} \mathrm{mean} = \cfrac{1}{N} \sum_{i=1}^{N} X_i \end{equation} for median?
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Find data and confidence “ellipses” (regions?) for a bivariate median?

I'm wondering about ways to compute data and confidence ellipses around a bivariate median. For example, I can easily compute a data ellipse or a confidence ellipse for the bivariate mean of the ...
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54 views

How to prove that medians were swapped?

I have two independed samples: df and df8. The first sample df includes points at the data1 and at the data2. These points were earned in an experimental group (n1=20). The second sample df8 includes ...
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Limitations of dividing the median of one arm in K-M analysis with the hazard ratio to get a “smoothened” estimation of the median of the other arm?

I am not statistician but use statistic measures in my work in regulatory medicine. A commonly used outcome measure in medicine is median survival by Kaplan-Meier (K-M) analysis. It sometimes happens ...
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34 views

Mann-Whitney test W statistics

Below is Mann-Whitney test result from Minitab. At the end of result, there is no p-value but "Cannot reject since W is < 363.0". What does it mean? I cannot ...
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Employment Term Likelihood

I have research information advising the median employment term for an executive is 4.8 years.I need to know what is the % likelihood of an executive staying for 5 years+- thanks for help
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If the mean and median underestimate the true central tendency, why use them?

In skewed distributions, both the mean and the median can easily underestimate or overestimate the true central tendency. For example, have a look at this violin plot: The median is shown here in ...
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Variability of the reference data and its effect on the transformed values

I conducted a study to compare two different tests at two different ages (children). Based on the previous literature we had hoped that the scores should be better (low score) with age but this was ...
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89 views

Calculate median for count data

I've got data that looks like this: ...
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920 views

How to calculate the median of a pdf

I'm new to statistics and I'm struggling to solve a question from an assignment. I have a probability density function and I need to calculate its median Here is the function: $$f(x) = 2xe^{-x^2}, x&...
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Should I treat my data as ordinal or interval?

I conducted a survey where I asked respondents how much they reduced their financial overhead, based on the following options: 0% (coded as 0 in my dataset) 1-10% (coded as 1) 11-25% (coded as 2, ...
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57 views

Is the sample mean a better point estimate of the population median than the sample median?

A beginner's question to check I've understood correctly. A basic stats textbook says: "The variance of the sampling distribution of the median is greater than that of the sampling distribution of ...
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Collapse FDR value of probes detecting the same gene

I'm very new in Microarray analysis, so I hope my question wouldn't be too irritating to you all. I have pre-processed and filtered my microarray datasets and perform differential expression analysis. ...
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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 $f(x)$ ...
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Best way to calculate a specific median

I have a strange question about calculating median. Context : I have a listing with people who subscribe to an insurance : They subscribe from DATE A to DATE B (at date B, they leave because they ...
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alternative way to compute or infer median from survival curve

I have used the survival package in R to generate survival plots. However for one of my sub groups, the graph does not fall below 0.5 survival. Good news for them......
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Explaining Mean, Median, Mode in Layman's Terms

How would you explain the concept of mean, median, and mode of a list of numbers and why they are important to somebody with only basic arithmetic skills? Let's not mention skewness, CLT, central ...
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Confidence interval for the median - continued

I have a set of values $x_i\quad i=1,…,N$ of which I can calculate the median M. Each $x_i$ has an error $\delta x_i$. The $x_i$ values are the result of a maximum likelyhood estimation and their ...
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66 views

How to compute difference in location computed in Mann-Whitney-test?

I would like to reproduce the results of the Wilcoxon-Mann-Whitney-test in R wilcox.test(x,y,paired=FALSE, conf.int=TRUE. I succeed to get the W-value but didn't ...
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Calculating mean and maximum with open ended bins

I am using excel and I need to work out the average lives of machinery as well as the maximum life. However all I have is the number of machines over ten years and the number of machines under 10 ...
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39 views

How does one find the sample median of for a group of iid random variables with Laplace distribution?

I know a median is $$\frac{1}{2} = \int_{-\infty}^{\mu} f(x)dx$$ I understand how to solve this for simple distributions. However, I am learning how to do it for iid samples, which I haven't done ...
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519 views

Confidence interval for the median

I have a set of values ${x_i}, i=1, \dots ,N$ of which I calculate the median M. I was wondering how I could calculate the error on this estimation. On the net I found that it can be calculated as $1....
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How much sense does median of one number make?

Median of one number = the number itself. I am calculating the median price sq ft of properties of different areas based on the different data entries I have got that include their ID, area and ...
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When the dependent variable is Median Time of a specific event, have we to use Quantile Regression or OLS Regression works well?

I am asked to make a regression model and the dependent variable is Median Time of a specific event. I think I can consider the Median Time of that event as a random variable and therefore the ...
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Calculating median for different subsets and sample sizes

I have a basic question about calculating median. The database I'm using contains registered records of criminals and the number of committed crimes per year each has committed in country X. Based on ...
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Calculating Median of Different Data Groups?

Bear with me here. I'm a newbie at this. Let's say we have this data : ...
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Is there a reliable nonparametric confidence interval for the mean of a skewed distribution?

Very skewed distributions such as the log-normal do not result in accurate bootstrap confidence intervals. Here is an example showing that the left and right tail areas are far from the ideal 0.025 ...
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When the Median Absolute Deviation (MAD) is zero

Suppose my data look like the following: (10, 10, 10, 10, 10, 0) Would it be possible to remove an outlier in this distribution using the median absolute deviation? Of course, you wouldn't need to ...
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28 views

Reducing density of outliers

I have a dataset with right skewed data. It represent frequency of candidates vs their TTB (which is essentially the number of days) Now the TTB values less than 14 or so are possible. But not ...
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Why is the 95% CI for the median supposed to be $±1.57*IQR/\sqrt{N}$?

In various sources (see e.g. here), the following formula is given for confidence interval for median (especially for the purpose of drawing notches on box-and-whisker plots): $$ 95\%\ CI_{\rm median}...
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Why use a “truncated mean” (aka “trimmed mean”)?

NB: In this post, I will use the abbreviation $TM_P$ to stand for a symmetric truncated (or trimmed) mean that discards the largest and smallest $P/2$ percent of the data. In fact, for concreteness I ...
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(CDF Quantile) Understanding an example from a swirl lesson

I need to understand an explanation from a swirl() lesson in course "Statistical Inference", menu option "Probability2". At 76% of completion, there is a question: "The quantile v of a CDF is the ...
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Probability of median of numbers in a range

how to calculate the probability that median of 3 random numbers from 0 to n, that are not in [0.2n, 0.8n] ? I think it should me P(2 numbers < 0.2n) + P(2 numbers > 0.8n) + P(all numbers < 0.2n ...
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Does the asymptotic distribution of sample median follow from statistical functionals?

I know that if $F_n$ is the empirical distribution function and $F$ is the true distribution function, then, with $T$ being any statistical functional (satisfying the von-Mises derivative conditions), ...
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35 views

Statistical analysis on daily data

I have a number of data points that I am trying to extract a meaningful pattern from (or derive an equation that could then be predictive). I am trying to find a correlation (?) between RANK and DAILY ...
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median split procedure reference

Is there any reference that I might use when I mention the median split method in a paper? i.e. turning a continuous variable into a categorical one by splitting a sample into 2 (above and below the ...
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Theil–Sen estimator in R with more than one variable? [duplicate]

Can Theil-Sen be defined for multiple linear regression? If so, is there an implementation in R for it? I simply want a formula a~b+c, but the package ...
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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, ...
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Filtered Data for Median - strange?

I am looking at a legacy process for work. We look at corporate budget data. The data is composed of annual budgets for different major categories for different corporate regions. The upper management ...