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Questions tagged [interquartile]

The interquartile range or midspread is a central interval containing 50% of the data, eliminating the 25% smallest and 25% largest observations.

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Control chart control limits for non-normal data

I have the following control chart: To my understanding, control limits are calculated with μ ± 3σ. So basically it's setting boundaries using three standard deviations - and this assumes that the ...
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Get a plausible distribution from quartiles and mean

I have the 3 quartiles and the mean of the incomes of a population, I would like to get from those a "regular" distribution, there might be several theoretical solutions but I just need a plausible ...
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IQR based outlier detection with multivariate data

One method to detect outliers in a dataset $[x_1 ... x_N], x_i \in R$ consists in finding the samples $x_i$ such that $$ x_i \lt Q_1-K*IQR | x_i \gt Q3 + K*IQR $$ where $Q_1$ and $Q_3$ are the first ...
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Quartile dummy effect analysis across two samples

I have two large cross-sectional samples, one for each of two products listed on ebay. i want to measure the effect of seller "feedback score" on auction revenue and suspect a diminishing effect. I ...
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Percentile calculation for binary voting system

Consider a system like Tinder for example where users can vote yes or no to a profile (like or dislike). If Tinder wanted to come up with an internal percentile rating of a user based only on the ...
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489 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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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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How to calculate the 4th quartile from median and IQR?

How can I calculate the 4th quartile from median and IQR. In a scientific article, I have those values: The median is 2.8 ng/ml of bisphenol A and The interquartile range, they wrote that 1.5-5.6. ...
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255 views

Transform a variable to desired Median and IQR

I am looking for a method to transform a variable ($Y_{old}$) into a new variable ($Y_{new}$) with a target median ($Median_{new}$) and IQR ($IQR_{new}$). The following transformation seems to work, ...
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1k views

How are whiskers in a Boxplot of different lengths? [duplicate]

The formula for calculating the position of the whiskers is Q3+1.5IQR and Q1-1.5IQR But doesn't that mean that the length of the whiskers should be of the same length? How are they of different ...
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2k views

IQR is 0 but mean is not 0

I have a dataset where the 5 number summary is: ...
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How to determine distribution from Sleep data min/max/mean values in R? [duplicate]

I want to determine the distribution from the EMFIT QS sleep data which gives only min, max and ...
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63 views

Is it valid to average IQR values?

I am interested in quantifying the dispersion of pixel values in one image. More specifically, I want to get an average value of dispersion of the image column-wise (i.e., compute the dispersion of ...
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4k views

What does the IQR/median mean?

What does IQR/Med tell you about the data? What is the purpose of dividing the IQR by the Median? Examples: ...
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1answer
686 views

Variance/standard deviation versus interquartile range (IQR)

Variance and interquartile range (IQR) are both measures of variability. But IQR is robust to outliers, whereas variance can be hugely affected by a single observation. Since variance (or standard ...
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1k views

1.5 IQR in finding outliers [closed]

What motivates the choice of 1.5 IQRs for finding outliers in a set of data? The the lower quartile minus 1.5 times the IQR would give the lower fence, and the upper quartile plus 1.5 times the IQR ...
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How to interpret interquartile range?

I have two categories of DVDs: 'Feature Films' and 'Children's Film and TV'. The IQRs of their prices are £6.50 and £3.50 respectively. What would the interquartile range show overall?
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Inter-quartile range

If we have a non-normal distribution say (Weibull) and we used a robust estimator of standard deviation in term of inter-quartile range (IQR). Is it possible we replace IQR=3*SD?
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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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Box plot for Likert scale 1 to 5: How is maximum equal to upper quartile? [duplicate]

I need to know how to interpret each of the graphics.
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1answer
20k views

Determine outliers using IQR or standard deviation?

Similar to ... which doesn't have the answer I'm looking for. The data set has a normal distribution. For the project I'm working on, outliers have to be determined over residuals of breeding data....
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1answer
67 views

Reference for the use of moving upper quartile window

I used a moving upper quartile window to select some data, but I require some kind of reference justifying its use and I cannot find anything suitable for it. Does anyone know of a book/paper that ...
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1answer
621 views

Comparing variability of likert scale answers beyond IQR

I am analysing a simple study where users were asked questions on 5-point likert scales. I use interquartile range (IQR) to assess the variability in the answers of the respondents. In particular, I ...
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Outlier Detection on skewed Distributions

Under a classical definition of an outlier as a data point outide the 1.5* IQR from the upper or lower quartile, there is an assumption of a non-skewed distribution. For skewed distributions (...
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Can the mean lie outside the the interquartile range (Q1 and Q3)? and if so what does it do to the distribution

Can the mean lie outside of the interquartile range? I realize that extreme outliers can affect or pull the mean, but can it pull the mean outside of the interval from the first quartile to the third ...
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Estimating necessary sample size

I am pretty new to statistics and I'd like to get pointers on the correct way to do this. I have a dataset in which I'm interested in the 50th and 90th percentile. I'd like to take a sample of that ...
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7k views

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 ...
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1answer
8k views

Find interquartile range of these data

Take these data: 5, 8, 9, 14 R says the interquartile range is 3: ...
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1answer
995 views

Error on interquartile range

How can I compute the error on the interquartile range of a sample? By error I mean its std deviation (e.g. error on the mean = $\frac{RMS}{\sqrt{N}}$. The sample is from a unimodal distribution, ...