Question

in the data set below, what are the lower quartile, th
1 1 3 3 4 6 8 8 8 9
lower quartile =
median =
upper quartile =

Explanation:

Step1: Sort the data

The data set is already sorted: \(1,1,3,3,4,6,8,8,8,9\)

Step2: Find the median

Since \(n = 10\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th values. \(\frac{n}{2}=5\), \(\frac{n}{2}+1 = 6\). The 5th value is \(4\) and the 6th value is \(6\). Median \(=\frac{4 + 6}{2}=5\)

Step3: Find the lower quartile

The lower half of the data is \(1,1,3,3,4\). Since \(n_1=5\) (odd), the lower quartile is the \(\frac{n_1 + 1}{2}\)th value. \(\frac{5+1}{2}=3\)rd value. Lower quartile \(=3\)

Step4: Find the upper quartile

The upper half of the data is \(6,8,8,8,9\). Since \(n_2 = 5\) (odd), the upper quartile is the \(\frac{n_2+1}{2}\)th value. \(\frac{5 + 1}{2}=3\)rd value. Upper quartile \(=8\)

Answer:

lower quartile \(=3\), median \(=5\), upper quartile \(=8\)