Interquartile range (IQR)

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Interquartile range (IQR): The interquartile range (IQR) is a measure of variability, based on dividing a data set into quartiles. Quartiles divide a rank-ordered data set into four equal parts. The values that divide each part are called the first, second, and third quartiles; and they are denoted by Q1, Q2, and Q3, respectively.

  1. Q1 is the “middle” value in the firsthalf of the rank-ordered data set. At Q1, 25% of values lie below and 75% values lie above this point
  2. Q2 is the median value of dataset, 50% of the values lie above and below this point
  3. Q3 is the “middle” value in the second half of the rank-ordered data set. At Q3, 75% of values lie below and 25% values above this point

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Interquartile is a measure of statistical dispersion, being equal to the difference between 75th and 25th percentiles, or between upper and lower quartiles, IQR = Q3 − Q1. In other words, the IQR is the first quartile subtracted from the third quartile.

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