Answer:
Q1 = 33
Q3 = 49.75
D2 = 28.4
D8 = 29.6
67th percentile = 46.10
Step-by-step explanation:
Given the data:
13 13 13 20 26 28 30 34 34 34 35 35 36 37 38
41 41 41 45 46 47 47 49 52 54 54 56 62 67 82
The first quartile (Q1) ;
1/4(n + 1)
Where n = number of observations
n = 30
Q1 = 0.25(30 + 1) = 0.25 × 31 = 7.75
7 : corresponds to 30
0.75 : (34 - 30) × 0.75 = 4 × 0.75 = 3
30 + 3 = 33
Third quartile (Q3) :
3/4(n + 1)
Where n = number of observations
n = 30
Q3 = 0.75(30 + 1) = 0.75 × 31 = 23.25
23 : corresponds to 49
0.25 : (52 - 49) × 0.25 = 3 × 0.25 = 0.75
49 + 0.75 = 49.75
Determine the second decile and the eighth decile.
Second decile (D2)
((n+1) × (2)) / 10
= (30 + 1)(2)/10 = 6.2
6 : corresponds to 28 +
0.2 : (30 - 28 )× 0.20 = 0.4
28 + 0.4 = 28.4
Eight decile (D8)
((n+1) × (8)) / 10
= (30 + 1)(8)/10 = 24.8
24 : corresponds to 52 +
0.8 : (54 - 52 )× 0.80 = 1.6
28 + 1.6 = 29.6
67th percentile :
67% × n = 0.67 × 30 = 20.10
20: corresponds to 46
0.1 : (47 - 46) × (0.1) = 0.1
46 + 0.1 = 46.10
