Question

Diketahui data sebagai berikut.
Data Frekuensi
50 - 54 = 3
55 - 59 = 12
60 - 64 = 16
65 - 69 = 14
70 - 74 = 5
Tentukan:
a. nilai Q₁, Q₂, dan Q₃,
b. jangkauan antarkuartil, serta
c. simpangan kuartil.
Jawab: ......​

Answer 1

Penjelasan dengan langkah-langkah:

a.

[tex]rumus \: kuartil \: ke \: -i \\ qi = bbqi + \frac{ \frac{i}{4} n - fkjs}{fqi} \times p \\ q1 = 54.5 + \frac{ \frac{1}{4} \times 50 - 3}{12} \times 5 \\ = 54.5 + \frac{ 9.5}{12} \times 5 \\ = 58.4[/tex]

[tex]q2 = 59.5 + \frac{ \frac{2}{4} \times 50 - 15}{16} \times 5 \\ = 59.5 + \frac{15}{16} \times 5 \\ = 62.6[/tex]

[tex]q3 = 64.5 + \frac{ \frac{3}{4} \times 50 - 31}{14} \times 5 \\ = 64.5 + \frac{6.5}{14} \times 5 \\ = 66.8[/tex]

b. Jangkauan antar kuartil = Q3-Q1= 66,8-58,4= 8,4

c. simpangan kuartil= 1/2 jangkauan antar kuartil = 1/2x 8,4= 4,2