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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 second quartile value (same as the median) is determined by 11×(2/4) = 5.5, which rounds up to 6. Therefore, 6 is the rank in the population (from least to greatest values) at which approximately 2/4 of the values are less than the value of the second quartile (or median). The sixth value in the population is 9. 9 Third quartile The third ...
The midhinge is related to the interquartile range (IQR), the difference of the third and first quartiles (i.e. IQR = Q 3 − Q 1), which is a measure of statistical dispersion. The two are complementary in sense that if one knows the midhinge and the IQR, one can find the first and third quartiles.
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 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.
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The interquartile mean (IQM) (or midmean) is a statistical measure of central tendency based on the truncated mean of the interquartile range.The IQM is very similar to the scoring method used in sports that are evaluated by a panel of judges: discard the lowest and the highest scores; calculate the mean value of the remaining scores.