Question

in the data set below, what are the lower quartile, the median, and the upper quartile? 4 6 7 9 9 9 lower quartile = median = upper quartile =

Explanation:

Step1: Sort the data (already sorted)

The data set is $4,6,7,9,9,9$.

Step2: Find the median

There are $n = 6$ data - points. The median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$. The median $M=\frac{7 + 9}{2}=8$.

Step3: Find the lower half

The lower half of the data set is $4,6,7$.

Step4: Find the lower quartile

Since there are 3 data - points in the lower half, the lower quartile $Q_1$ is the middle value of the lower half, so $Q_1 = 6$.

Step5: Find the upper half

The upper half of the data set is $9,9,9$.

Step6: Find the upper quartile

Since there are 3 data - points in the upper half, the upper quartile $Q_3$ is the middle value of the upper half, so $Q_3 = 9$.

Answer:

lower quartile = 6
median = 8
upper quartile = 9