Question

in the data set below, what are the lower quartile, the median, and t
19 30 37 42 50 69 69 70 70 93 95
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: \(19,30,37,42,50,69,69,70,70,93,95\). The median is \(69\).

Step2: Find the lower quartile

The lower half of the data (excluding the median) is \(19,30,37,42,50\). The number of values \(n_1=5\). The lower quartile is the \(\frac{n_1 + 1}{2}\) -th value.
\(\frac{5+1}{2}=3\) -th value. The lower quartile is \(37\).

Step3: Find the upper quartile

The upper half of the data (excluding the median) is \(69,70,70,93,95\). The number of values \(n_2 = 5\). The upper quartile is the \(\frac{n_2+1}{2}\) -th value.
\(\frac{5 + 1}{2}=3\) -th value. The upper quartile is \(70\).

Answer:

lower quartile \(=37\)
median \(=69\)
upper quartile \(=70\)