# 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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### 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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### 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 ...