Answer:
Xbar = 20.813
Median = 19.95
5 - number summary :
Minimum = 15.2
Q1 = 19.05; Q2 = 19.95 ; Q3 = 21.95 ; maximum = 29.4
Standard deviation, s = 4.068
Step-by-step explanation:
Given the data:
X : 15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4
Ordered data:
15.2, 18.8, 19.3, 19.7, 20.2, 21.8, 22.1, 29.4
The mean (xbar) :
Xbar = Σx / n ; n = sample size = 8
Xbar = 166.8 / 8 = 20.8125
Xbar = 20.813
The median :
1/2 *(n+1)th term
1/2(9) = 4.5
(4 + 5)th term / 2
(19.7 + 20.2) / 2 = 19.95
The five number summary :
Minimum = 15.2
Lower quartile (Q1) = 1/4(9) = 2.25 ; (2nd + 3rd) term / 2
(18.8 + 19.3) / 2 = 19.05
Median (Q2) = 19.95
Upper quartile (Q3) :
3/4(9) = 6.75 = (6th + 7th) / 2
(21.8 + 22.1) / 2 = 21.95
Maximum = 29.4
The standard deviation, s = sqrt[(x - xbar)²/ (n-1)]
Using calculator ;
s = 4.068
