1. A fertilizer mixing machine is set to give 12kg of nitrate for every 100Kg bag of fertilizer. A sample of ten such bags is examined. The percentages of nitrates are as follows:
11, 14, 13, 12, 13, 12, 13, 14, 11, 12.
a. Calculate
i. The sample mean
ii. Sample standard deviation s
Answers
Given : A fertilizer mixing machine is set to give 12kg of nitrate for every 100Kg bag of fertilizer. A sample of ten such bags is examined
Solution:
11, 14, 13, 12, 13, 12, 13, 14, 11, 12.
Number of Bags = 10
Sum of all = 11 + 14 + 13 + 12 + 13 + 12 + 13 + 14 + 11 + 12 = 125
Mean = 125/10 = 12.5
sample mean = 12.5
sample standard deviation = √( ∑ (x - Mean)²/(N - 1))
N = Number of observation
population standard Deviation = √ (∑ (x - Mean)²/N )
(11-12.5)² + (14-12.5)² + (13-12.5)² + (12-12.5)² + (13-12.5)² + (12-12.5)² + (13-12.5)² + (14-12.5)² + (11-12.5)² + (12-12.5)²
∑ (x - Mean)² = 10.5
sample standard deviation = √(10.5)/9 = 1.08
population standard Deviation = √(10.5)/10 = 1.025
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