Question

what is the upper and lower quartile of this set of data?
15, 19, 20, 25, 31, 38, 41

• lower quartile: 19

upper quartile: 25

• lower quartile: 25

upper quartile: 38

• lower quartile: 19

upper quartile: 38

• lower quartile: 15

upper quartile: 41

Explanation:

Step1: Identify median (Q2)

Data is ordered: $15, 19, 20, 25, 31, 38, 41$. Median is the 4th value: $25$.

Step2: Split data for quartiles

Lower half: $15, 19, 20$; Upper half: $31, 38, 41$.

Step3: Find lower quartile (Q1)

Median of lower half: 2nd value, $19$.

Step4: Find upper quartile (Q3)

Median of upper half: 2nd value, $38$.

Answer:

lower quartile: 19
upper quartile: 38