Question

in the data set below, what are the lower quartile, the median, and the upper quartile?
17 22 37 54 54 55 59 71 74 81 87
lower quartile =
median =
upper quartile =

Explanation:

Step1: Confirm sorted data set

Data: $17, 22, 37, 54, 54, 55, 59, 71, 74, 81, 87$

Step2: Find median (middle value)

Position: $\frac{11+1}{2}=6$th value
Median = $55$

Step3: Split data into lower half

Lower half: $17, 22, 37, 54, 54$

Step4: Calculate lower quartile

Lower quartile = middle of lower half = $37$

Step5: Split data into upper half

Upper half: $59, 71, 74, 81, 87$

Step6: Calculate upper quartile

Upper quartile = middle of upper half = $74$

Answer:

lower quartile = $37$
median = $55$
upper quartile = $74$