Answer:
The variability in endotoxin concentration is far greater in urban homes than in farm homes.
Yes, The fourth spreads do communicate the same message as the standard deviations did.
Step-by-step explanation:
Given the data:
U: 6.0 5.0 11.0 33.0 4.0 5.0 89.0 18.0 35.0 17.0 23.0
F: 4.0 14.0 11.0 9.0 9.0 8.0 4.0 20.0 5.0 8.9 21.0 9.2 3.0 2.0 0.3
Farm sample:
Σx = 128.4
Σx² = 1617.94
n = 15
Sample mean, m = Σx / n ; 128.4 / 15 = 8.56
Standard deviation :
sqrt[(Σx²/n-1) - (m²)]
sqrt[(1617.94/14) - (8.56^2)]
sqrt(42.293542) = 6.50
Fourth spread = 3rd quartile - 1st quartile
3rd quartile = 3/4(n+1)th term
1st quartile = 1/4(n+1)th term
Using calculator :
Q3 = 11 ; Q1 = 4
Fourth spread = 11 - 4 = 7
Urban sample:
Σx = 246.0
Σx² = 11600
n = 11
Sample mean, m = Σx / n ; 246 / 11 = 22.36
Standard deviation :
sqrt[(Σx²/n-1) - (m²)]
sqrt[(11600/10) - (22.36²)]
sqrt(660.0304) = 25.69
Fourth spread = 3rd quartile (Q3) - 1st quartile(Q1)
3rd quartile = 3/4(n+1)th term
1st quartile = 1/4(n+1)th term
Q3 = 33 ; Q1 = 5
Fourth spread = 33 - 5 = 28
Standard deviation of farm sample = 6.50
Standard deviation of urban sample = 25.69
From the standard deviation values obtained, it could be observed that the urban sample has greater Variability than the farm sample, this is due to the higher standard deviation value of the urban sample and this shows that variation about the mean value is higher for urban sample.
Looking at the fourth spread value for both urban and farm samples ; the fourth spread value for urban is greater Than for farm sample.
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