Answer: 22.5 ; 5 ; 14
Explanation:
Given the dataset:
{20,22,23,24,26,26,28,29,30}
The lower quartile (Q1) = 1/4(n + 1)th term
Where n = number of observations, n = 9
Q1 = 1/4 (9 + 1)th term
Q1 = 1/4(10) = 2.5
We average the 2nd and 3rd term:
(22 + 23) / 2
45 / 2 = 22.5
B) The interquartile range(IQR) of the dataset :
{62,63,64,65,67,68,68,68,69,74}
IQR = Q3 - Q1
The lower quartile (Q1) = 1/4(n + 1)th term
Where n = number of observations, n = 10
Q1 = 1/4 (10 + 1)th term
Q1 = 1/4(11) = 2.75 term
We take the average of the 2nd and 3rd term:
(63 + 64) / 2
45 / 2 = 63.5
The upper quartile (Q3) = 3/4(n + 1)th term
Where n = number of observations, n = 10
Q3 = 3/4 (10 + 1)th term
Q3 = 3/4(11) = 8.25 term
We take the average of the 8th and 9th term:
(68 + 69) / 2
137 / 2 = 68.5
IQR = Q3 - Q1
IQR = 68.5 - 63.5
IQR = 5
C) give the dataset :
{7,8,8,9,10,12,13,15,16}
The upper quartile (Q3) = 3/4(n + 1)th term
Where n = number of observations, n = 9
Q3 = 3/4 (9 + 1)th term
Q3 = 3/4(10) = 7.5 term
We take the average of the 7th and 8th term:
(13 + 15) / 2
28 / 2 = 14