Questions tagged [range]

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

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Is there a meaning to the integral of $x \times f(x)$ over a range that is not infinite?

I know that the expected value can be computed as : $\mathbb{E}(X) = \int_{-\infty}^{\infty}xf(x)dx$ What if we do not do the integral over the whole range but only up to some value? Would there be ...
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How can I find the start of a range in an automated way?

I am looking at real estate sales data for different regions. I bin the data by sold price range in 1000 increments (see below). I am looking to find the start of the price range or cluster in which ...
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Show that Sample Mean and Sample Range are independently distributed for a random sample from Normal Distribution

Let $X_{1},\ldots {, X_{n}}$ be iid random variables with $X_{1} ∼ N(µ,\sigma ^{2}).$Let $\bar{X}= \sum_{i=1}^{n} \frac{X_{i}}{n}$, $R=max_{1\le i \le n} \{X_{i}\}$-$min_{1\le i \le n}\{X_{i}\}$.Show ...
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How did Acheson Duncan calculate degrees of freedom for ranges in his d2* table?

As found in Acheson Duncan, Quality Control and Industrial Statistics (and earlier), there is a table for d2* for estimating the variance from the range based on the number of subgroups and the ...
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How to deal with imputed values outside the definition range? (Using softImpute e.g.)

When using imputation algorithms, we sometimes know that the missing data is subject to certain properties. For example, we might have the typical Netflix problem, where we have a sparse matrix of ...
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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 : $$...
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How to break up the following scale into equal segments?

In Excel, there is a conditional formatting feature like this: Let's say in order to figure out what color to use for a value, I split the gradient into 14 steps, such as: Red:6Parts,Yellow:0Parts ...
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Estimators for range and nugget parameters extremely correlated

When fitting a generalised least squares (GLS) model to a spatial dataset, I was surprised to find how correlated the estimators for the range and nugget are. I was assuming a covariance matrix $\...
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Expanding range of data (for PCA)

I am interested in computing 5 indices of structural connectivity between 116 different brain regions, and their associations with behavioural performance. I plan on using prinicipal component ...
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Determine what range represents 95% of a skewed data set

I have a set of reference wetlands and experimentally manipulated wetlands and I am comparing many water quality variables between them. My thought was to first identify which of the manipulated ...
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Can you recommend neural network suitable for finding minimum and maximum of numbers in list with some noisy data?

Let's have a list of integer numbers. These are generated about some "center" value with some tolerance +/-. I call this the "range". Also - there is some noise - the numbers are ...
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Practical use for heritability value at sub-population level?

For me as a layperson, heritability is something that much smarter people than me calculate, and there are several questions already on the forum about how to do that (eg, this and this). I ...
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2 answers
212 views

How to "squish" a range of numbers to the same spread between 0 and 1

So I have a range of numbers that I need to "squish" into values between 0 and 1 - where lowest value is zero and the highest is 1. I need preserve the ratio. For instance. If I had these ...
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Given the range $R$ of $n$ data points, what is the range of these points' standard deviation? [duplicate]

Given the range $R$ ($= max - min$) of $n$ data points ($x_1, x_2, ..., x_n$), what is the range of these points' standard deviation $\sigma$? It's easy to see that the min value of $\sigma$ can be $0$...
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How to find the bound of a time dependent variable?

I am working on modeling my problem statistically and I need to Know the bound or range of my variable. It is a time series variable position(t) where position(t+1) = position(t) + a.X - (1-a).Y a is ...
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Why won't my xgBoost regressor predict above a certain value, even though it sees higher in training?

I have created my first xgboost regressor. I input some self collected data, which I scale using sklearn's standardScaler. The model is trained on approximately 25,000 samples, and then tested on ...
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In computing the range of raw scores, if the lowest value is 0. Should I still use it as my lowest value to find the range?

My professor gave us the raw scores. We need to find the range. The highest value is 93 and the lowest is 0. Here's the raw scores 66,85,40,5,12,12,18,23,1,15,1,6,81,50, 21,0,27,5,13,0,24,22,5,1,32,12,...
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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 ...
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93 views

Marginal distributions given the distribution of range

I'm working with an upper diagonal distribution whose distance from the diagonal is Lomax Pareto (Type II) distribution. The distance of a point from the diagonal line y = x is $\frac{\sqrt{(x_0-y_0)^...
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How do I properly weight an uneven (spacing) distribution of the numbers? [closed]

I have a set of numbers (depths actually) and I need to take the mean of another variable over these depths. For example, take the mean of temperature over a range of depths, however these depths are ...
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Descriptive measures

What is the percentage of people who earned between Rs 75 and Rs 125? If the given frequency table is below:
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Calculate mean from range

Suppose we have data points like How can we calculate mean from this dataset
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What is the distribution of sample's range, obtained from a normal distribution?

Let $x$ is a normally distributed variable: $x\sim N(\mu,\sigma$). I wonder, the distribution of the range. I mean, let we have a sample(let size $n$) from the above distribution. Let define $...
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Any other way to calculate range of transformed variable?

I have been doing questions related to transformations of 2d random variables. In a question I have to find a range for $$u = (x-y)/2 $$ and $$v = y $$ where $x,y > 0$ So is it necessary that ...
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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 ...
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If a false positive rate of α is desired, what is the acceptable range of false positives one would expect from a sample size of n?

For instance, suppose I design a test to have a false positive rate of 5%. I am going to perform this test on what is assumed to be an all negative population. If my sample size was 20, I would expect ...
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2 votes
3 answers
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Find Q1 and Q3 from median and IQR

A study gives the following: $n = 67$ mean = 73 sd = 68 median = 55 IQR = 66 Is it possible from this information to get the actual Q1 and Q3 values? I used the $n$, mean & sd to get 95% ...
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Convert negative to positive percentage range into 1-10 scale

I know how to convert a range of positive % numbers into any positive integer scale, but am having trouble figuring out how to do it when my % range includes negative %s. Example: I have the ...
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How to scale data to desired range? [duplicate]

I have a table with 3 columns X, Y and Z with n rows. The range of the data is 0-255. But I wished to scale the values such that the range becomes from -p to +q (where I decide p and q). I randomly ...
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What are the broadest class of distributions for which the range statistic is ancillary to the expectation of the random variable?

Let $X_1,X_2,X_3$ be iid random variables such that $E(X_1)=\mu$ Define $X_{(3)}$ and $X_{(1)}$ as the maximum and minimum order statistics respectively. I know that if $X$ is normal, $R=X_{(3)}-X_{...
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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., $\max(x_i) - \min(x_i)$? ...
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3 votes
2 answers
136 views

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 ...
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15 votes
1 answer
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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: ...
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1 vote
1 answer
138 views

Expected value of CDF evaluated at sample min/max, with respect to sample size

I've been using simulation to investigate the behavior of cumulative density function evaluated at extreme values of a sample. Functionally, my study has $n$ instrumented fish migrating downstream ...
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3 votes
3 answers
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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 ...
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1 answer
432 views

What does range in descriptive statistics mean

What does high range in my variable mean??. If I have a variable whose range is less ,what does it mean??
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Newbie wondering about standard deviation and how to detect outliers in new datapoints

So I have a dataset, with the count of records processed per day in each, e.g. | 27th April: 3491 | 28th April: 2058 | 29th April: 9321 | 30th April: 1021 I want to be able to take a new day's count ...
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1 vote
1 answer
705 views

Significance of correlation with range restriction in x

Background Range restriction can happen in various study designs and it affects the results of bivariate correlation or in multiple regression, for example. In some cases the range restriction may be ...
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1 answer
110 views

Name for Standard Deviation over possible range (1-255)?

I have RGB brightness values over a possible range of 1-255. I am already computing Coefficient of Variation, but since my domain is strictly limited, I am interested in seeing a measure of how spread ...
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correlation with small range of data

I have two count variables. I want to calculate a Pearson correlation between them. However one of the variables only has a rangge of 1-7. Is it inadvisable to use Pearson correlation to study a ...
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2 votes
1 answer
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multivariate normal distribution range [duplicate]

Simple question about MVN pdf. I understand the domain to be [0,1]. However, why does scipy.stats.multivariate_normal.pdf output values above this range. E.g. <...
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155 views

How is this mean scale score range calculated?

I have the attached report for a standardized test (data in the report is simulated). I'm wondering how the column Mean Scale Score Range is calculated. Do the lines indicate the limits of 95% of ...
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2 votes
1 answer
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Normalize an array of numbers to specific range

How can I normalize an array of values (e.g., {0, 3, 4, 7, 9, 13, 22}) to a range of [12, 24]?
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2 votes
1 answer
31 views

Mean nonequality test if data are intervals

If $X, Y$ are two sets of observations of two random scalar (univariate) variables, one can determine if the expected values of the two variables are unequal, with appropriate tests. My question is: ...
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4 votes
1 answer
3k views

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 ...
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2 answers
368 views

Does changing the point range of items of a construct measured through likert scale affect in any way validity and reliability of the construct?

I am using a pre-existing universal tested scale to measure a specific construct. The construct is measured through 5 items on a 5 points likert scale. However, I would probably need to change the ...
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0 answers
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How to create a dynamic range?

I have data for the entire last year. It is simply a value of a variable for every minute, grouped by days. What I need to do is take all this data and define a dynamic range - that is, define two ...
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359 views

Comparing ranges of different groups

I have data that's like as follows $A : 133-134$ $B : 131-135$ $C : 135-148$ I have to check if $A$ is more "similar" to $B$ or $C$ where similarity is defined as smallest "distance" between the ...
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1 vote
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5k views

How to normalize data using Interquartile range?

I am trying to normalize a dataset using the Interquartile range (IQR), I've already gotten the value of IQR, which is Q3 -Q1 (difference between 75th and 25th percentiles), what should I do then? For ...
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2 answers
2k views

Why does Mean deviation = Standard deviation = Range/2?

We know that mean deviation and standard deviation are two different things but why are both of them equal to Range/2? Range ($R$) = Highest value - lowest value Mean deviation ($\text{MD}$) = ...
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