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grequantworld.blogspot.com http://grequantworld.blogspot.com/2009/08/what-is-average-arithmetic-mean-of-all.html What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive? What is the average (arithmetic mean) of all the multiples of ten from 10 to 190 inclusive? A. 90 B. 95 C. 100 D. 105 E. 110 Solution: Arithmetic mean of all the multiples of ten from 10 to 190 inclusive is given by sum of all the multiples from 10 to 190 / 19 ==> sum = 10+20 + 30 ..190==> take 10 as common ==> 10 (1+2+3+4 ...19) Arithmetic mean = 10 (1+2+3+4 ...19) /19 Sum of n consecutive number is given by n(n+1)/2 ==> 19(20)/2 A.M = 19(20)/2 *10/19 ==> 100

Arithmetic Mean of All the Multiples of Ten From 10 to 190

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Arithmetic Mean of All the Multiples of Ten From 10 to 190

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What is the average (arithmetic mean) of all themultiples of ten from 10 to 190 inclusive?

What is the average (arithmetic mean) of all the multiples of ten f rom 10 to 190 inclusive?

A. 90B. 95C. 100D. 105E. 110

Solution:

Arithmetic mean of all the multiples of ten f rom 10 to 190 inclusive is given by sum of all themultiples f rom 10 to 190 / 19 ==>

sum = 10+20 + 30 ..190==> take 10 as common ==> 10 (1+2+3+4 ...19)

Arithmetic mean = 10 (1+2+3+4 ...19) /19

Sum of n consecutive number is given by n(n+1)/2 ==> 19(20)/2

A.M = 19(20)/2 *10/19 ==> 100