# 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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### 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 - ...
88 views

### 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 ...
29 views

### 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 &...
113 views

### 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 ...
89 views

### 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 ...
54 views

### 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 ...
26 views

### 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 ...
16 views

### 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 ...
103 views

### 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 ...
40 views

### 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?
301 views

### 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% ...
141 views

### 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 ...
94 views

### 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 $O(skewness^2)$. ...
194 views

### 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 ...
293 views

### 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 ...
153 views

### 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 ...
229 views

### 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 ...
130 views

### 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 ...
2k 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 ...
3k 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 ...
6k views

### 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. ...
471 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, ...
2k 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 ...
6k views

### IQR is 0 but mean is not 0

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

### 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 ...
70 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 ...
7k 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: ...
2k 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 ...
2k 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 ...
20k views

### 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?
73 views

### 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?
5k views

### 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}...
449 views

### 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.
28k 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....
92 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 ...
981 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 ...
42k views

### 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 (...
7k views

### 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 ...
34 views

### 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 ...
11k 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 ...
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, ...