The idea when using quartiles is take all your data and write it out in increasing order then divide it in 4 equal parts.The upper
quartile is the part containing the highest data values, the upper
middle quartile is the part containing the next-highest data values,
the lower quartile is the part containing the lowest data values,
while the lower middle quartile is the part containing the next-
lowest data values.
Here is the catch-------------- the terms can also refer to cut-off values between the 4 sets.
The term 'upper quartilevcan be
cut-off value between the upper quartile subset and the upper middle
quartile subset. And, the 'lower quartile' can refer to a cut-off value between the lower quartile set
and the lower middle quartile set. usually we look at the interquartile range (IQR) which is the range between the thrird and 1st quartile
IQR is used to make box plots and other cool graphs.
The upper quartile (Q3) is the median of the upper half of the data set. Q3 cuts off highest 25% of data And just FYI: first quartile (designated Q1) = lower quartile = cuts off lowest 25% of data = 25th percentile second quartile (designated Q2) = median = cuts data set in half = 50th percentile
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Interquartile Range, or IQR
Consider the data: 1, 2, 2, 3, 4, 4, 5, 7, 11, 13 , 19 (arranged in ascending order) Minimum: 1 Maximum: 19 Range = Maximum - Minimum = 19 - 1 = 18 Median = 4 (the middle value) 1st Quartile/Lower Quartile = 2 (the middle/median of the data below the median which is 4) 3rd Quartile/Upper Quartile = 11 (the middle/median of the data above the median which is 4) InterQuartile Range (IQR) = 3rd Quartile - 1st Quartile = 11 - 2 = 9
In a data sample, the purpose of quartile deviation is a way to measure data dispersion instead of using the range. The quartile deviation is found by subtracting the lower quartile from the upper quartile, and dividing this result by two.
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Because the IQR excludes values which are lower than the lower quartile as well as the values in the upper quartile.