Question

the data set represents the total number of tuba players in each of 11 different school bands.
0, 1, 3, 3, 4, 4, 4, 5, 6, 6, 8
what is the lower quartile of the data?
○ 1
○ 3
○ 4
○ 6

Explanation:

Step1: Order the data (already ordered)

The data set is \(0, 1, 3, 3, 4, 4, 4, 5, 6, 6, 8\) with \(n = 11\) values.

Step2: Find the median position

The median position is \(\frac{n + 1}{2}=\frac{11+ 1}{2}=6\)th value. The median is the 6th value, which is \(4\).

Step3: Split data into lower half

The lower half of the data (values before the median) is \(0, 1, 3, 3, 4\) (5 values).

Step4: Find lower quartile (Q1)

For the lower half (5 values), the median (Q1) is the \(\frac{5 + 1}{2}=3\)rd value. The 3rd value in \(0, 1, 3, 3, 4\) is \(3\).

Answer:

3 (corresponding to the option "3")