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5 students of a class have an average height 150 cm and variance 18 cm². A new student, whose height is 156 cm, joined them. The variance (in cm²) of the height of these six students is:

1. 20
2. 18
3. 16
4. 22

Correct answer: 20

Solution

Sum x^2 = 5*(18+150^2)=112590. Add 156: new sum=906, mean=151, sum x^2=112590+24336=136926. New variance = 136926/6 - 151^2 = 22821-22801 = 20.

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