The mean (arithmetic mean) that the $11$ numbers in a perform is $14$. If the typical of $9$ of the number in the list is $9$, what is the mean of the other $2$ numbers?


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Survey the Question

Let’s find the difficulty for clues regarding what it will certainly be testing, as this will help change our minds to think around what kind of math knowledge we’ll use to fix this question. Pay attention to any kind of words the sound math-specific and also anything special about what the number look like, and mark them on our paper.

You are watching: The average of the 11 numbers in a list is 14

The concern revolves about the average that a perform of numbers, so it most likely tests ours Numerical methods for explicate Data mathematics skill. Let’s store what we’ve learned about this ability at the guideline of ours minds as we approach this question.

What perform We Know?

Let’s carefully read through the question and also make a perform of the things that we know.

The typical of $11$ number is $14$The average of $9$ of this numbers is $9$We want to understand the median of the other $2$ numbers

Develop a Plan

The inquiry asks around averages, so let’s begin by recalling our equation because that calculating the typical of a team of numbers.

$$Average = Sum of Values/Number of Values$$

So for example, if the sum of $10$ numbers is $200$, then the median of those $10$ numbers is $200/10$, or $20$. Regarded a slightly various way, if the typical of $10$ numbers is $20$, then the amount of those $10$ number is $200$. We have to keep our minds flexible as soon as it pertains to sums and averages. Some concerns it’ll be much easier to work-related with sums, whereas for other questions it’ll be much easier to occupational with averages.

Questions that provide us an median of a collection of numbers and also an typical of a subset of the bigger collection of numbers tend to be much easier to deal with if us think of sums rather of averages because that those numbers. Here, we understand that if we have actually the sum of the “other $2$ numbers,” then we can just division that amount by $2$ to gain the mean of those $2$ numbers. And if us look closely, us have sufficient information to number out the sum of the other $2$ numbers, since:

$$Sum of 9 Numbers + Sum of Other 2 Numbers = Sum of 11 Numbers$$


From our equation v sum and also average, we understand that the amount of a collection of number is the number of values multiplied by the average. For this reason from this us get:

$$Sum of 9 Numbers = ;9·9 ;;= 81$$$$;Sum of 11 Numbers = 11·14 = 154$$

Let’s usage these two sums to uncover the sum, and then the average, the the other $2$ numbers.

Solve the Question

So if all $11$ numbers sum up to $154$ and $9$ of the numbers sum up to $81$, climate the other $2$ numbers must add up to the difference between these 2 sums:

$$Sum of Other 2 Numbers = 154-81=73$$

And if the two numbers have a sum of $73$, climate their typical must it is in $73/2=36.5$. For this reason the exactly answer is $36.5$.

What Did we Learn

For questions entailing averages, we have to keep our minds flexible. There’s a an excellent probability the the question could be more easily resolved if we transform the averages to sums. Let’s remember the just since a concern is worded a particular way, the doesn’t pigeonhole us into only gift able to think of the concern that way.

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