Statistical Analysis Stack Exchange
Statistical Analysis Stack Exchange

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.

Wikipedia has an article with further references.

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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 (Exponential, Poisson, Geometric, etc) is the best way to…
Eric
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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} = {\rm Median} \pm \frac{1.57\times…
Ilya V. Schurov
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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 deviation) is a more complicated measure to…
LondonRob
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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. We want to remove data which is most likely…
Bas
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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 quartile?
bob
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Distribution-free confidence interval for IQR

I am looking for a way to calculate confidence intervals for the interquartile range IQR of a numerical variable. Of course, they can be found by the bootstrap, but I am explicitly looking for a different, still distribution-free way. Since the IQR…
Michael M
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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. Can I conclude that the first quartile is 1.5 the…
Doris TAN
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How are whiskers in a Boxplot of different lengths?

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 lengths in some boxplots?
ricksanchez
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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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IQR is 0 but mean is not 0

I have a dataset where the 5 number summary is: Min. 1st Qu. Median Mean 3rd Qu. Max. -0.0082630 0.0000000 0.0000000 0.0000059 0.0000000 0.7966557 I'm not quite sure how to visualize this/whether this is even…
shoestringfries
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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: IQR = 3.0 Med = 8.1 IQR/Med = .37 IQR = 2.1 Med = 7.1 IQR/Med = .29 I got the numbers from this site. I understand IQR and…
NAK
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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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Find interquartile range of these data

Take these data: 5, 8, 9, 14 R says the interquartile range is 3: IQR(c(5, 8, 9, 14)) # 3 ...but I make it 5. What am I doing wrong? Here are the steps I've taken: Find median, which is 8.5 Split the data around the median into two groups, like…
luciano
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Properties of a "mean", computed using weighted sum of quartiles

I've stumbled upon a paper (Eq. 1) that computes a "statistically robust mean" of a distribution using the following formula: $EM = \frac{1}{2} Q_2 + \frac{1}{4} (Q_1 + Q_3)$ where $Q_{1, 2, 3}$ are first, second and third quartiles of the…
alex.melkonyan
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ANOVA for median and interquartile range

I have 5 samples of different sizes (5000-15000 observations each) from 5 (presumably different) distributions. I need to perform something like ANOVA to test the hypothesis that these distributions have the same median and interquartile range. If I…
zlon
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