find the median, first quartile (q1) and the third quartile (q3) for the data shown, which is already…

Explanation:

Step1: Find the median

For a set of $n = 11$ (odd - numbered) data points, the median is the $\left(\frac{n + 1}{2}\right)$-th value. $\frac{11+ 1}{2}=6$. So the median is the 6 - th value in the sorted data set, which is $13.3$.

Step2: Find the first quartile ($Q1$)

The lower half of the data set contains the first 5 values (since $n = 11$, the lower half is the first $\frac{n - 1}{2}=5$ values). For a set of 5 (odd - numbered) values, the median of this lower - half (which is $Q1$) is the $\left(\frac{5 + 1}{2}\right)$-th value. $\frac{5+1}{2}=3$. So $Q1$ is the 3 - rd value in the lower half of the data set, which is $6.6$.

Step3: Find the third quartile ($Q3$)

The upper half of the data set contains the last 5 values. For a set of 5 (odd - numbered) values, the median of this upper - half (which is $Q3$) is the $\left(\frac{5 + 1}{2}\right)$-th value. $\frac{5 + 1}{2}=3$. So $Q3$ is the 3 - rd value in the upper half of the data set. The upper half of the data set is ${15.1,16.5,23,28.3,28.9}$, and $Q3$ is $23$.

Answer:

Median: $13.3$ $Q1:6.6$ $Q3:23$