Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 1 2 2 3 3 4 7 8 9 9 9 lower quartile = median = upper quartile =

Explanation:

Step1: Find the median

The median is the middle value of a data set. For a data set with \(n = 11\) values (odd - numbered), the median is the \(\frac{n + 1}{2}\)th value.
\(\frac{11+ 1}{2}=6\)th value.
The data set is \(1,2,2,3,3,4,7,8,9,9,9\). The 6th value is \(4\).

Step2: Find the lower quartile

The lower half of the data set is \(1,2,2,3,3\). For a data set with \(n = 5\) values (odd - numbered), the lower quartile is the \(\frac{n + 1}{2}\)th value of the lower half.
\(\frac{5+1}{2}=3\)rd value. The 3rd value of the lower half \(1,2,2,3,3\) is \(2\).

Step3: Find the upper quartile

The upper half of the data set is \(7,8,9,9,9\). For a data set with \(n = 5\) values (odd - numbered), the upper quartile is the \(\frac{n + 1}{2}\)th value of the upper half.
\(\frac{5 + 1}{2}=3\)rd value. The 3rd value of the upper half \(7,8,9,9,9\) is \(9\).

Answer:

lower quartile \(=2\)
median \(=4\)
upper quartile \(=9\)