Question # 1: Find the first, second and third quartile of the followingungroupe
ID: 2918272 • Letter: Q
Question
Question # 1:
Find the first, second and third quartile of the followingungrouped data:
92.01, 83.90, 74.70, 48.60, 58.05
Question # 2:
Find the coefficient of correlation for the following data,
x
y
9
28.4
15
29.3
24
37.6
30
36.2
38
36.5
46
35.3
53
36.2
60
44.1
64
44.8
76
47.2
Question # 3:
Calculate the least square regression equation of Y on X for thefollowing data.
X
5 6 8 10 12 13 15 16 17
Y
16 19 23 28 36 41 44 45 50
x
y
9
28.4
15
29.3
24
37.6
30
36.2
38
36.5
46
35.3
53
36.2
60
44.1
64
44.8
76
47.2
Explanation / Answer
Answer:
Find the first, second andthird quartile of the following ungrouped data:
92.01, 83.90, 74.70, 48.60, 58.05
Sorted: 48.60, 58.05, 74.70, 83.90, 92.01
We know that;
n = 5
Q1 = (n+1)/4 th value
Q1 = (5+1)/4
Q1 = (6)/4
Q1 = 1.5th value
Q1 = 1st value + 0.5 * (2nd value –1st value)
Q1 = 48.60 + 0.5 * (58.05 – 48.60)
Q1 = 48.60 + 0.5 * (9.45)
Q1 = 48.60 + 4.725
Q1 = 53.33 is the first quartile.
Q2 = 2(n+1)/4 th value
Q2 = (n+1)/2
Q2 = (5+1)/2
Q2 = (6)/2
Q2 = 3rd value
Q2 = 74.70 is our second quartile ormedian.
Q3 = 3(n+1)/4 th value
Q3 = 3(5+1)/4
Q3 = 3(6)/4
Q3 = 18/4
Q3 = 4.5th value
Q3 = 4th value + 0.5 * (5th value –4th value)
Q3 = 83.90 + 0.5 * (92.01 – 83.90)
Q3 = 83.90 + 0.5 * (8.11)
Q3 = 83.90 + 4.055
Q3 = 87.955 is our third quartile or 75% of the datapoint.