find q1 of the following data set.\n3, 9, 12, 4, 6, 40, 25, 14, 10\n\na. 5\nb. 10\nc. 19.5\nd. 14.5

Explanation:

Step1: Sort the data set

$3,4,6,9,10,12,14,25,40$

Step2: Calculate the position of Q1

The formula for the position of the first - quartile ($Q1$) is $i=\frac{n + 1}{4}$, where $n$ is the number of data points. Here $n = 9$, so $i=\frac{9+1}{4}=\frac{10}{4}=2.5$.

Step3: Interpolate to find Q1

Since $i = 2.5$, $Q1$ is between the 2nd and 3rd ordered data - points. The 2nd value is $4$ and the 3rd value is $6$. Using the interpolation formula $Q1=x_2+(i - 2)(x_3 - x_2)$, we have $Q1=4+(2.5 - 2)(6 - 4)=4 + 0.5\times2=5$.

Answer:

A. 5