Question 141

Arithmetic mean of 56, 57, 58, ..., 100 is:

Solution

Arithmatic mean=$$\ \frac{sumof observations }{ total no. Of observations}$$

sum of first n natural no.=$$\ \frac{n(n+1)}{ 2}$$

sum of first 100 natural no.=$$\ \frac{100*101 }{2 }$$=5050

sum of first 55 natural no.=$$\ \frac{55*56}{2 }$$=1540

sum of 56,57,...…,100=5050$$\ \ \ -\ $$1540

=3510

Arithmatic mean=$$\ \frac{3510 }{45 }$$=78

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