35) Find the Variance and standard deviation
xi 2 4 6 8 10 12 14 16
fi 4 4 5 15 8 6 4 5
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Answer:
15.08
3.88
Step-by-step explanation:
xi 2 4 6 8 10 12 14 16
fi 4 4 5 15 8 5 4 5 ∑fi 50
xifi 8 16 30 120 80 60 56 80 ∑fixi = 450
Mean = 450/50 = 9
Variance = σ² = (4 * (-7)² + 4(-5)² + 5(-3)² + 15(-1)² +8(1)²+ 5(3)²+4(5)²+5(7)² )/50
= ( 196 + 100 + 45 + 15 + 8 + 45 + 100 + 245)/50
= 754/50
= 15.08
Standard Deviation = σ = √15.08 = 3.88
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