Question

in the data set below, what are the lower quartile, the median, and the upper quartile?
1 1 2 2 3 5 5 5 5 8
lower quartile =
median =
upper quartile =

Explanation:

Step1: Find the median (Q2)

The data set has 10 values, which is even. The median is the average of the 5th and 6th values. The 5th value is 3, the 6th is 5. So median $=\frac{3 + 5}{2}=4$.

Step2: Split data for quartiles

Split the data into lower half (first 5 values: 1, 1, 2, 2, 3) and upper half (last 5 values: 5, 5, 5, 5, 8).

Step3: Find lower quartile (Q1)

Lower half has 5 values (odd), so Q1 is the 3rd value of the lower half: 2.

Step4: Find upper quartile (Q3)

Upper half has 5 values (odd), so Q3 is the 3rd value of the upper half: 5.

Answer:

lower quartile = 2
median = 4
upper quartile = 5