Question

find the median, first quartile (q1) and the third quartile (q3) for the data shown, which is already sorted. the number of data is n = 10. do not round your answers. x 1.9 2.8 3.8 7.3 13.7 18.4 19.8 23.7 24.5 29.4 median = q1 = q3 =

Explanation:

Step1: Find the median

For $n = 10$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered values. $\frac{n}{2}=5$ and $\frac{n}{2}+1=6$. Median $=\frac{13.7 + 18.4}{2}=\frac{32.1}{2}=16.05$.

Step2: Find the first quartile ($Q_1$)

The lower half of the data set is the first 5 values: $1.9,2.8,3.8,7.3,13.7$. Since $n = 5$ (an odd - numbered data set), the first quartile $Q_1$ is the $\frac{n + 1}{2}$th value. $\frac{5+1}{2}=3$rd value. So $Q_1 = 3.8$.

Step3: Find the third quartile ($Q_3$)

The upper half of the data set is the last 5 values: $18.4,19.8,23.7,24.5,29.4$. Since $n = 5$ (an odd - numbered data set), the third quartile $Q_3$ is the $\frac{n + 1}{2}$th value. $\frac{5 + 1}{2}=3$rd value. So $Q_3=23.7$.

Answer:

Median = $16.05$
$Q_1 = 3.8$
$Q_3 = 23.7$