What is the average (arithmetic mean) of all the multiples of ten from

Question

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

fizzywah · Answer

10 and 190 inclusive would mean there are 19 terms.

No need to add up all the terms and further divide by 19 since the terms are evenly spaced in ascending order from 10, 20, 30........190

The middle term is the average which is the tenth term = 100

C is the answer.

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nalinnair · Answer

The multiples of ten from 10 to 190 inclusive would be an evenly spaced set with 19 terms - 10, 20, 30,.......190
So average = (First term + Last Term)/2 = (10 + 190)/2 = 200/2 = 100
Hence, the correct answer is C.

law258 · Answer

190/10 = 19 --> there are 19 multiples of 10 (i.e. there are 19 numbers in the set)

19/2 = 9... --> so we're looking for the 10th number in the set because it's an odd number of numbers in the set.

100 is the 10th number in the set.

Thus, C is correct.

Abhishek009 · Answer

All the multiples of ten from 10 to 190 inclusive = 10 + 20 + 30 + 40........190

10 + 20 + 30 + 40........190 = 10 ( 1 + 2 + 3 ....... 19 )

Now, ( 1 + 2 + 3 ....... 19 ) = 19*20/2 => 190

So, The sum of the series is 10*190

Average of the series will be 10*190/19 = 100

Hence answer will be (C) 100

Heseraj · Answer

Bunnel,

I have a question regarding this question: Can we say since this data set (the multiples of 10) is equally distributed and the two lower and upper limits included in the data set, bringing the total data points to  an odd number , therefore the average will be equal to the middle number:   100  ? 
IE: 12345 what is the average: 3

Bunuel · Answer

Multiples of 10 represent arithmetic progression (aka evenly spaced set). In any evenly spaced set the  arithmetic mean (average) is equal to the median  and can be calculated by the formula  mean=median=\frac{a_1+a_n}{2} , where  a_1  is the first term and  a_n  is the last term.

First term is 10 and last term is 190. So  mean=median=\frac{10+190}{2}=100 .

Answer: C.

JeffTargetTestPrep · Answer

We can calculate the average using the following formula for evenly spaced sets:

average = (first multiple in the set + last multiple in the set)/2

average = (10 + 190)/2 = 200/2 = 100

Answer: C

Mega1234 · Answer

Sum of arithmetic series = n(a+l)/2 , where n= number of terms, a = first term, l= last term

Average = sum/n

Using both the equations, average = (a+l)/2
=> 200/2 = 100, option C

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What is the average (arithmetic mean) of all the multiples of ten from

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