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The three quartiles, resulting in four data divisions, are as follows: The first quartile (Q 1) is defined as the 25th percentile where lowest 25% data is below this point. It is also known as the lower quartile. The second quartile (Q 2) is the median of a data set; thus 50% of the data lies below this point.
These quartiles are denoted by Q 1 (also called the lower quartile), Q 2 (the median), and Q 3 (also called the upper quartile). The lower quartile corresponds with the 25th percentile and the upper quartile corresponds with the 75th percentile, so IQR = Q 3 − Q 1 [1]. The IQR is an example of a trimmed estimator, defined as the 25% trimmed ...
We can solve this by using a weighted average of the quartiles and the interquartile dataset: Consider the following dataset of 9 observations: 1, 3, 5, 7, 9, 11, 13, 15, 17. There are 9/4 = 2.25 observations in each quartile, and 4.5 observations in the interquartile range.
Splitting the observations either side of the median gives two groups of four observations. The median of the first group is the lower or first quartile, and is equal to (0 + 1)/2 = 0.5. The median of the second group is the upper or third quartile, and is equal to (27 + 61)/2 = 44. The smallest and largest observations are 0 and 63.
The middle three values – the lower quartile, median, and upper quartile – are the usual statistics from the five-number summary and are the standard values for the box in a box plot.
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional mean of the response variable across values of the predictor variables, quantile regression estimates the conditional median (or other quantiles) of the response variable.
The third quartile value for the original example above is determined by 11×(3/4) = 8.25, which rounds up to 9. The ninth value in the population is 15. 15 Fourth quartile Although not universally accepted, one can also speak of the fourth quartile. This is the maximum value of the set, so the fourth quartile in this example would be 20.
The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles. The use of the term "hinge" for the lower or upper quartiles derives from John Tukey 's work on exploratory data analysis in the late 1970s, [ 1 ] and "midhinge" is a fairly modern term dating from around that time.