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The second quartile (Q 2) is the median of a data set; thus 50% of the data lies below this point. The third quartile (Q 3) is the 75th percentile where lowest 75% data is below this point. It is known as the upper quartile, as 75% of the data lies below this point. [1]
Third quartile (Q 3 or 75th percentile): also known as the upper quartile q n (0.75), it is the median of the upper half of the dataset. [ 7 ] In addition to the minimum and maximum values used to construct a box-plot, another important element that can also be employed to obtain a box-plot is the interquartile range (IQR), as denoted below:
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 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 ]
The 25th percentile is also known as the first quartile (Q 1), the 50th percentile as the median or second quartile (Q 2), and the 75th percentile as the third quartile (Q 3). For example, the 50th percentile (median) is the score below (or at or below, depending on the definition) which 50% of the scores in the distribution are found.
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. The two unusual percentiles at either end are used because the locations of all seven values will be approximately equally spaced if the data is normally ...
The upper middle class consists of those in the 60th to 80th percentile of household income. The median net worth is nearly double that of the middle class. Average net worth for the upper class
First quartile The first quartile is determined by 11×(1/4) = 2.75, 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 third value in the population is 7. 7 Second quartile