Answer:
Range = 32 ; IQR = 13 ; Variance = 92.75 ; Standard deviation = 9.63
Step-by-step explanation:
Given the data:
28, 42, 58, 48, 45, 55, 60, 49, 50
Reorderd data: 28, 42, 45, 48, 49, 50, 55, 58, 60
The range: maximum - minimum
Range = 60 - 28 = 32
Interquartile range (IQR) : Q3 - Q1
Q3 = 3/4(n+1) th term. ; n = sample size
Q1 = 1/4(n+1)th term.
Using calculator :
Q3 = 56.5 ; Q1 = 43.5
IQR = 56.5 - 43.5 = 13
The variance :
Σ(X - m)^2 / n-1
m = Σx / n
Mean, m = 435 / 9 = 48.33
Variance :
[(28-48.33)^2 + (42-48.33)^2 + (45-48.33)^2 + (48-48.33)^2 + (49-48.33)^2 + (50-48.33)^2 + (55-48.33)^2 + (58-48.33)^2 + (60-48.33)^2] / 8
= 742.0001 / 8
= 92.75
Standard deviation = sqrt(Variance):
Sqrt(92.75) = 9.63
C.)
Sample mean are very close with a slightly greater Variability in the air quality of Anaheim over Pomona
