Question

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

Explanation:

Step1: Arrange data in ascending order

The data set is already in ascending order: 0, 1, 3, 3, 4, 4, 5, 6, 6, 8

Step2: Calculate the position of the lower - quartile

The formula to find the position of the lower - quartile ($Q_1$) for a data set of size $n$ is $L=\frac{n + 1}{4}$ when $n$ is the number of data points. Here, $n = 10$. So, $L=\frac{10+ 1}{4}=2.75$.

Step3: Interpolate to find $Q_1$

The 2nd value is 1 and the 3rd value is 3. Using interpolation, $Q_1=1+(3 - 1)\times0.75=1 + 1.5=2.5$

Answer:

2.5