Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

Questions tagged [range]

range is the difference between the largest and smallest data value.

Wikipedia has an article with further information and references.

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Relationship between the range and the standard deviation

In an article I found the formula for the standard deviation of a sample size $N$ $\sigma=\frac{\overline{R}}{2.534}$ where $\overline{R}$ is the average range of subsamples (size $6$) from the main sample. How the number $2.534$ is calculated?…
Andy
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What is the name for the average of the largest and the smallest values in a given data set?

What do you call a statistical mean that is calculated from upper and lower extremes in any given dataset? For example, if you have a set: { -2, 0 , 8, 9, 1, 50, -2, 6} The upper extreme of this set is 50 and lower extreme is -2. So, average of the…
blackbeard
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Independence of Sample mean and Sample range of Normal Distribution

Let $X_1,\dots,X_n$ be i.i.d. random variables with $X_1 \sim N(\mu,\sigma^2)$. Let $\bar X =\sum_{i=1}^n X_i/n$ and $R = X_{(n)}-X_{(1)}$, where $X_{(i)}$ is the $i$ the order statistic. Show that $\bar X$ and $R$ are independently distributed. I…
A.D
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Median > Mode > Mean > Range

My question is: Is there a set of data which allow the median to be larger than the mode, the mode to be larger than the mean and the mean to be larger than the range? If so, is there a pattern, or a specific characteristic of a dataset to allow…
BlueSigma
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How to visualize a range (min/med/max)?

I'm looking for a visually compelling yet immediately understandable way to visualize a range of data (min, median, max) Considerations: The approach should be understandable to a wide variety of people Ideally, would allow for the comparison to…
user49598
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What is meant by the interquartile range of ordinal data?

It is commonly said that the interquartile range (IQR) is suitable to describe ordinal-, interval- and ratio-level data (one of many examples found on the Internet). But calculating the IQR includes finding the difference between two values, and…
jon1000
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Is there a relation between sample size and variable range?

I have done simulations with different sample sizes of a normal distribution (mean=0, sd=10) and plotted the number of samples against statistical parameters. I understand that the relation of sample size and mean, sd and the relative frequency of…
user128020
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Min and max range from standard deviation

If I have 2 data points like 16.70 (+/-4.33) 54.70 (+/-16.30) where 16.7 = mean and +/- 4.33 is the standard deviation, is it possible to calculate a range out of that? I would think that roughly, the min range here would be 16.7-4.33 and the max…
poshtad
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Negative inner fence. How can you find the outlier using 1.5 x IQR?

I'm trying to find outliers using 1.5 x interquartile range but I'm getting a negative value for the lower bound. I found Q3 and Q1 which are 13.30 & 3.00 respectively but for the lower bound i get -12.45 which seem odd. Is there something I'm doing…
user55794
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Asymptotic value of an integral related to distances in a unit n-ball

In trying to find out the pdf of the range $T$ of euclidean distances of $m$ randomly and uniformly chosen points from the origin in an $n$-dimensional unit ball, I have obtained the following : $$ f(t)=m^2.n(n-1)\int_0^{1-t}…
sajjad veeri
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Why do we add an extra decimal place when we calculate the range in statistics?

From Mario Triola's textbook: I understand that we add a decimal place when we calculate the median (it is possible to have (a+b)/2 ). I absolutely do NOT understand why we do that when we round off the range. It's just a subtraction, a simple…
Iaroslav Baranov
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Unbiased estimator of standard deviation

I'm reading "Properties of range-based volatility estimators" where the authors talk about using the range of a distribution ($h$ - $l$) to estimate its volatility. Specifically, they say, Daily return $c$ is a random variable drawn from a normal…
housecat64
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Distribution of ranges of normally distributed variables

I have four independent variables $x_i$, each of them normally distributed with $\mu = 0$ and $\sigma = 1$. What is the distribution of the range of the four variables, i.e., $\max(x_i) - \min(x_i)$? For example, I draw a random sample of $n=10000$…
user1618022
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Statistical dispersion metric for single extreme value

I have around a million sets of 8 datapoints. I would like to rank these sets of 8 data points. I am trying to identify sets where there is a single extreme value and the other 7 datapoints are of similar value. For example, $\{0.2, 0.19, 0.27,…
Harry Stuart
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How to calculate a confidence interval for a series of Bernoulli Trials?

I have to test if a event have a p probability of happening. I can run this event as much times I like (given it can be run by a computer). So I was searching a way to test if the probability of this event is in an acceptable range for my case. How…
Bruno Andreetto
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