# 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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### Why divide data into 4 parts for IQR, and not into parts of 20 or 10 percentages each?

Why divide data into 4 parts for IQR, versus into more parts, such as 20 or 10 percent per part? I know that interquartile range by definition means 25%, but that is not my question. I think that ...
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### How do I regress income quartiles against each other?

I'm looking to find out whether an attitude differs across income quartiles. My supervisor has mentioned dummy coding and regressing the quartiles against each other, however, I'm sort of at a loss as ...
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### Are there cases where we need to avoid the usage of IQR?

Let's consider the interquartile range (IQR), the standard deviation (SD) and the mean absolute deviation (MAD). We know that "one of the most common robust measures of scale is the interquartile ...
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### BEST POSSIBLE WAY to determine significantly high values within zero-inflated univariate continuous distributions

I have more than 50 different distributions, corresponding to 50 different kind of customers, who spend their money in a certain way within a period, being this amount the single variable of interest. ...
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### Interquartile range when back-transformed mean on log-scale is not equal to median on normal scale

I have 2x10 observations that follow a non-normal distribution. They are perfectly distributed on log-scale. From what I've learned, the back-transformation of the mean on log-scale should be a "...
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### Asymptotic efficiency of IQR

I was wondering about the asymptotic efficiency of the Interquartile Range (IQR) in the Gaussian case. I have calculated it empirically using a Monte Carlo estimator, and it appears to be equal to ...
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### Calculating Change in OR per increase from the 25th to 75th percentile (IQR)

I have a dichotomous outcome variable (ever disease) and a continuous exposure variable (chemical). I have already run the logistic regression for the ln exposure and gotten the odds ratio. However, ...
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### Replacing outliers with the median value of the preceding 5 observations

In the paper Implications of dynamic factor models for VAR analysis the authors propose a a technique for removing outliers in variables used for dyanamic factors analysis: "The outlier ...
1 vote
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### Calculating descriptive stats for aggregate/binned data [duplicate]

I have several datasets that I wish to analyse and summarize - and I'm starting with the basic median, and percentile/quartiles to begin with (unless there are other approaches I should be considering)...
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### Why is the Tukey's IQR not used in the R program?

I was writing an R Markdown for calculating measures of spread and was surprised to find that the IQR function does not use the IQR calculation I am used to using, ...
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### Comparing averages of non normal distributions

I want to compare the daily average revenue of a promotion period (7 days) of a business with the daily average of the rest of the year. So, sample 1 has 7 data points, whereas sample 2 has 300 data ...
1 vote
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### May the cumulative distribution function be used to calculate the inter-quartile range and vise-versa?

May the cumulative distribution function be used to estimate the inter-quartile range? I am drawing their similarities. The IQR is found via a boxplot which has percentiles. A percentile comes from ...
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### Interquartile ranges of 2 groups in meta analysis

I am performing a meta analysis of mutliple trials (Intervention vs. Placebo) and wanted to describe the baseline characteristics in a table. Some trials report continous variables as medians and ...
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### Standard deviation on Bimodal data

Standard deviation, whilst it is often used on normal distributions, is it a useful statistic on global temperature, both daily and yearly, given that weight of the data is towards the ends of the ...
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### Is it possible to calculate median value and interquatile range for a set of numbers containing a range or inequalities?

I am trying to make simple median and IQR calculations that involve numbers (in percentages) appearing in a range and inequalities in addition to whole numbers. My sample dataset looks like this: 5, ...
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### Using the IQR method to filter outliers in experimental research, by group or as a whole?

In my current dataset (results from a factorial ANOVA), I know I have outliers (due to qualitative comments participants wrote during an online experiment), thus I'd like to do a filtering process to ...
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### Are the position indices (quartiles, median, mean) of distribution in classes always different from those of the unit distribution?

Are the position indices (quartiles, median, mean) of distribution in classes always different from those of the unit distribution? If so, for what reason? In theory, since the class distribution is a ...
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### Is it valid to remove trials as outliers using IQR?

I have a repeated measures experiment where all participants completed several trials for each condition. My dependent variables are response time and accuracy. I am using the Interquartile Range as ...
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### Question regarding the IQR

I have a question regarding some homework for uni: The variable "number of points per game" has a mean of 25, a median of 30, and an interquartile range of 20. Which of the following ...
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### Should interquartile range (IQR) be reported as one number or as a range?

Is is there a standard how to report interquartile range (IQR)? It seems that different practices are used, some report it as one number and others as a range (25th and 75th percentile/quantile 1 - ...
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### How should I interpret the median and the interquartile range?

I have a 7 point Liker Scale, ranging from 1=Strongly disagree to 7=Strongly Agree that has the purpose to measure if the respondents recognize the logo of a brand. I estimated the median and the ...
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### Time to event analysis - median (IQR) is <75% experience event

I am plotting the Kaplan-Meier survivor function for time to event & will estimate the median survival. I want to present this with the IQR. If the resultant KM looks something like the below &...
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### representing quantile like quartile in form of normal distribution curve

I learned in statistics the first quartile, 2nd quartile, and 3rd quartile can be represented in the figure1 below I came across this part of the article Step 4 - Feature Engineering.In this portion ...
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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 ...
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### Significance Test for Interquartile Range

Is there a test that determines whether a statistically significant difference exists between the IQR of two or more independent sets of non-normally distributed continuous data? Let's say I have a ...
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### a box-and-whisker plot for the difference between two independent groups

I'm trying to plot a box-and-whisker plot for differences between samples obtained from two different (and presumably independent) groups (the sample numbers may differ between the groups). Because ...
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### Can I select custom quantiles to detect outliers using the IQR

The Interquartile Range is defined as: $IQR = Q_{3} - Q_{1}$, where $Q_{3}, Q_{1}$ define the lower and upper quartile. What if I want to detect fewer outliers? Can I define custom lower and upper ...
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### Method to determine outliers with a skewed dataset [duplicate]

How can we find outliers in a dataset with a (highly) skewed distribution? With a normal distribution, is it well documented to use 2 x Standard Deviation or the upper boundary of the box plot (1.5 x ...
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### Is there a convention for how to handle data points that fall on the fences when determining outliers?

If I have a data set where a given measurement is equal to Q1 - 1.5(IQR), is there a convention for how to handle this? Should this be considered an outlier?
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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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### Why can't we sum two interquartile ranges?

The interquartile range is defined as the difference between the third and first quartiles: $IQR = Q_3 - Q_1$ When studying intensive and extensive properties, only values of extensive properties ...
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### Estimating Quartiles with Moments

The Wikipedia article on Skewness indicates that the median of a distribution can be estimated from the mean, standard deviation, and skeweness with an error term that goes as $O(skewness^2)$. ...
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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 ...
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### What's the best method to measure relative variability for non normal data?

I have a set of data that states the volume required each month for the next 12 for 750 raw materials. I would like to determine the variability in the demand for each material, and categorise 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 ...
1 vote
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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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### 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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### 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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### 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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### 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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### IQR is 0 but mean is not 0

I have a dataset where the 5 number summary is: ...