Interquartile range (IQR) Flashcards
Interquartile range
The Interquartile range (also called the mid spread) is equal to the difference between the 3rd and 1st quartiles.
The median divides the data into two halves. For a set of n ordered numbers the median is the (n + 1) � 2 th value. In this case n = 11 so it is the 6th value. The 1st quartile divides the bottom half of the data into two halves, and the 3rd quartile divides the upper half of the data into two halves.
The 1st quartile (equivalent to the 25th percentile) is the (n + 1) � 4 th value. Which in this case is number 3 which is 67.
The 3rd quartile (equivalent to the 75th percentile) is the 3 (n + 1) � 4 th value. Which in this case is number 9 which is 89.
The interquartile range of this data set would therefore be 89 - 67 (Q3 - Q1) which is 22.
A percentile (or a centile) is a measure used in statistics indicating the value below which a given percentage of observations in a group of observations fall. For example, the 20th percentile is the value (or score) below which 20% of the observations may be found.
Since quartile divide a data set into quarters we can make some additional comments about the data.
75% of the data set is below Q3
50% of the data set is less than Q2
25% of the data set is below Q1
50% of the data set is between Q1 and Q3
Quartiles and ranges are useful, but they are also somewhat limited because they do not take into account every score in our group of data. To get a more representative idea of spread we need to take into account the actual values of each score in a data set. The variance and standard deviation are such measures.
