Question

Question about IQR(Interquartile Range)

1) could you please give some vivid example to explain what is IQR? like in what circumstance we use it and how to use it?

2) what's the difference and connection between quantile and quartile?

Thanks a lot

Answer 1

IQR:-

The interquartile range (IQR) is the difference between the first quartile and third quartile. The formula for this is:

IQR = Q₃ - Q₁

determining the interquartile range, we first need to know the values of the first quartile and third quartile

HOW TO AND WHY USE IQR:-

The range gives us a measurement of how spread out the entirety of our data set is. The interquartile range, which tells us how far apart the first and third quartile are, indicates how spread out the middle 50% of our set of data is.

primary advantage of using the interquartile range rather than the range for the measurement of the spread of a data set is that the interquartile range is not sensitive to outliers.

Due to its resistance to outliers, the interquartile range is useful in identifying when a value is an outlier.

The interquartile range rule is what informs us whether we have a mild or strong outlier. To look for an outlier, we must look below the first quartile or above the third quartile. How far we should go depends upon the value of the interquartile range.

QUARTILES AND QUANTILES:-

Quartiles Q1, Q2 and Q3 are three points that divide a distribution into 4 parts. Thus if X is any random variable, P( X <= Qi) = i/4 for i = 1,2,3.

On the other hand zp will be a quantile of order p if P(X <= zp) = p for 0 < p < 1.

Quantile is the generalization of quartile. Decile, percentile and quantile all are generalization of quartile. Increasing it means partionting the data in 4, 10, 100 parts. Whereas quantiles are refers to uncountable partition of data..