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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 third quartile (Q 3) is the 75th percentile where
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)
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.
In this example, only the first and the last number are changed. The median, third quartile, and first quartile remain the same. In this case, the maximum value in this data set is 89°F, and 1.5 IQR above the third quartile is 88.5°F. The maximum is greater than 1.5 IQR plus the third quartile, so the maximum is an outlier.
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
The IQR of a set of values is calculated as the difference between the upper and lower quartiles, Q 3 and Q 1. Each quartile is a median [8] calculated as follows. Given an even 2n or odd 2n+1 number of values first quartile Q 1 = median of the n smallest values third quartile Q 3 = median of the n largest values [8]
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 ...
A common collection of order statistics used as summary statistics are the five-number summary, sometimes extended to a seven-number summary, and the associated box plot. Entries in an analysis of variance table can also be regarded as summary statistics. [1]: 378