Question

what is quartile 1 of the data? 12,15,17,18,23,30

Explanation:

Step1: Arrange data in order

The data 12,15,17,18,23,30 is already in ascending - order.

Step2: Calculate position of Q1

The formula to find the position of the first quartile ($Q_1$) for a data - set of size $n$ is $L_{Q1}=\frac{n + 1}{4}$. Here, $n = 6$, so $L_{Q1}=\frac{6+1}{4}=1.75$.

Step3: Interpolate to find Q1

Since the position is 1.75, $Q_1$ is between the 1st and 2nd ordered data values. The 1st value is 12 and the 2nd value is 15. Using linear interpolation: $Q_1=12+(15 - 12)\times0.75=12 + 2.25=14.25$.

Answer:

14.25