Finding Impossible Averages in the Sequence 10,11,12,13,14: No-Calculator Method

Without calculating, choose the number that cannot be the average of the following group of numbers:

10,11,12,13,14 10,11,12,13,14

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:09 Let's find the incorrect average without doing any calculations.
00:14 First, plot the numbers on a number line.
00:18 The average should be about in the middle of these numbers.
00:23 This option is good because it's around the center.
00:27 This one is too small, so it can't be the average.
00:32 This option is good because it's around the center.
00:35 This option is good because it's around the center.
00:39 This option is good because it's around the center.
00:46 And that's how you find the solution to this question.

Step-by-step written solution

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1

Understand the problem

Without calculating, choose the number that cannot be the average of the following group of numbers:

10,11,12,13,14 10,11,12,13,14

2

Step-by-step solution

To solve this problem, let us examine the range of the numbers given:

The smallest number in the set is 10 10 , and the largest is 14 14 . Hence, any average of these numbers must fall within this range, i.e., between 10 and 14.

Considering the choices:

  • 12 12 is within the range 10 10 to 14 14 .
  • 9 9 is outside of this range.
  • 13 13 is within the range 10 10 to 14 14 .
  • 11 11 is within the range 10 10 to 14 14 .

Thus, it is clear that the number that cannot be the average of (10,11,12,13,14)(10, 11, 12, 13, 14) is 9 9 , as it does not lie within the required range.

3

Final Answer

9

Practice Quiz

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Calculate the average of \( 10 \) and \( 12 \).

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