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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.
The five-number summary is a set of descriptive statistics that provides information about a dataset. It consists of the five most important sample percentiles: the sample minimum (smallest observation) the lower quartile or first quartile; the median (the middle value) the upper quartile or third quartile; the sample maximum (largest observation)
In statistics, the quartile coefficient of dispersion (QCD) is a descriptive statistic which measures dispersion and is used to make comparisons within and between data sets. Since it is based on quantile information, it is less sensitive to outliers than measures such as the coefficient of variation .
This is the minimum value of the set, so the zeroth quartile in this example would be 3. 3 First quartile The rank of the first quartile is 10×(1/4) = 2.5, which rounds up to 3, meaning that 3 is the rank in the population (from least to greatest values) at which approximately 1/4 of the values are less than the value of the first 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 range , which enhances the accuracy of dataset statistics by dropping lower contribution, outlying points. [ 5 ]
For example, they require the median and 25% and 75% quartiles as in the example above or 5%, 95%, 2.5%, 97.5% levels for other applications such as assessing the statistical significance of an observation whose distribution is known; see the quantile entry.
There are 9/4 = 2.25 observations in each quartile, and 4.5 observations in the interquartile range. Truncate the fractional quartile size, and remove this number from the 1st and 4th quartiles (2.25 observations in each quartile, thus the lowest 2 and the highest 2 are removed). 1, 3, (5), 7, 9, 11, (13), 15, 17
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.