Question

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

Explanation:

Step1: Find the median

The data set has \(n = 11\) values. The median is the \(\frac{n + 1}{2}\)th value.
\(\frac{11+ 1}{2}=6\)th value.
The data set is \(1,1,1,1,1,2,4,7,9,9,9\). The \(6\)th value is \(2\).

Step2: Find the lower quartile

The lower half of the data set (excluding the median) is \(1,1,1,1,1\). The lower quartile is the \(\frac{5 + 1}{2}=3\)rd value of the lower - half. The \(3\)rd value of \(1,1,1,1,1\) is \(1\).

Step3: Find the upper quartile

The upper half of the data set (excluding the median) is \(4,7,9,9,9\). The upper quartile is the \(\frac{5+ 1}{2}=3\)rd value of the upper - half. The \(3\)rd value of \(4,7,9,9,9\) is \(9\).

Answer:

lower quartile \(=1\), median \(=2\), upper quartile \(=9\)