Question

Identify the lower quartile (Q1), the median (Q2), and the upper quartile (Q3) for this data set.

{1, 2, 4, 5, 7, 7, 8, 9, 9, 10}



Q1 = 1, Q2 = 7, Q3 = 10


Q1 = 4, Q2 = 7, Q3 = 9


Q1 = 2, Q2 = 8, Q3 = 8


Q1 = 4.5, Q2 = 7.5, Q3 = 9.5

Answer 1

{1, 2, 4, 5, 7, 7, 8, 9, 9, 10}

Lower Quartile: Q₁ = ¹/₄(n + 1)
Q₁ = ¹/₄(10 + 1)
Q₁ = ¹/₄(11)
Q₁ = 2³/₄

Median: Q₂ = ¹/₂(n + 1)
Q₂ = ¹/₂(10 + 1)
Q₂ = ¹/₂(11)
Q₂ = 5¹/₂

Upper Quartile: Q₃ = ³/₄(n + 1)
Q₃ = ³/₄(10 + 1)
Q₃ = ³/₄(11)
Q₃ = 8¹/₄

Q₁ = 2³/₄
Q₂ = 5¹/₂
Q₃ = 8¹/₄