Find the Average of 11, 8, 14, 20, 7: Mental Math Approach

Q: How can I estimate without calculating the exact sum?

Look for balance points! Notice that $ 20 $ is much higher than the others, so the average will be pulled above the middle value $ 11 $. Think of it like a seesaw!

Q: What if the numbers were more spread out?

The same strategy works! Extreme values (very high or low numbers) will pull the average toward them. Always consider which direction the outliers will shift your estimate.

Q: Is there a difference between average and median?

Yes! The median is the middle number when ordered ($ 11 $ here), but the average considers all values equally, so $ 20 $ pulls it higher to $ 12 $.

Q: How do I know which answer choice is most reasonable?

Eliminate extremes first! Since we have numbers from $ 7 $ to $ 20 $, the average must be between these values. Then consider if outliers pull it higher or lower than the middle.

Q: What if I'm still unsure between two close answers?

Think about symmetry. We have $ 7, 8 $ below $ 11 $ and $ 14, 20 $ above it. Since $ 20 $ is farther from $ 11 $ than $ 7 $ is, the average shifts upward.

Estimation with Central Tendency

Without calculating, choose the average of the following group of numbers:

$11,8,14,20,7$

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Mark the appropriate average, without calculating

00:03 Let's plot the numbers on the number line

00:20 The average should be approximately in the middle of the numbers

00:24 This option cannot be the average because it's too small

00:29 This number also doesn't fit, it's too large

00:35 The average should be approximately in the middle of the numbers

00:38 This number also doesn't fit, it's too large

00:42 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Without calculating, choose the average of the following group of numbers:

$11,8,14,20,7$

Step-by-step solution

To solve this problem, we'll employ reasonable estimation and logic:

Step 1: Identify the range of numbers, which is from 7 to 20.
Step 2: Consider that the average (mean) is typically near the middle of the list when the numbers are evenly distributed.
Step 3: Identify the number configuration: $7, 8, 11, 14, 20$ . Notice $11$ is close to the middle, but $20$ as an outlier pulls the average higher.

Reviewing the numbers:

11 and 14 are central, flanked by 8 and 7 on the lower side, and 20 on the upper side.
Hence, guess an average slightly above the median (11).

Since we're not calculating, a reasonable average looking at the numbers and distribution is $12$ .

The solution to the problem is thus $12$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Range Analysis: Identify lowest and highest values to establish boundaries
Visual Method: Order numbers 7, 8, 11, 14, 20 and find center
Check: Average should be between middle values 11 and 14 ✓

Common Mistakes

Avoid these frequent errors

Assuming the average equals the middle number
Don't just pick the middle value from the ordered list = wrong answer! The median (11) isn't the same as the mean because outliers like 20 pull the average higher. Always consider how extreme values affect the balance point.

Practice Quiz

Test your knowledge with interactive questions

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

FAQ

Everything you need to know about this question

How can I estimate without calculating the exact sum?

Look for balance points! Notice that $20$ is much higher than the others, so the average will be pulled above the middle value $11$ . Think of it like a seesaw!

What if the numbers were more spread out?

The same strategy works! Extreme values (very high or low numbers) will pull the average toward them. Always consider which direction the outliers will shift your estimate.

Is there a difference between average and median?

Yes! The median is the middle number when ordered ( $11$ here), but the average considers all values equally, so $20$ pulls it higher to $12$ .

How do I know which answer choice is most reasonable?

Eliminate extremes first! Since we have numbers from $7$ to $20$ , the average must be between these values. Then consider if outliers pull it higher or lower than the middle.

What if I'm still unsure between two close answers?

Think about symmetry. We have $7, 8$ below $11$ and $14, 20$ above it. Since $20$ is farther from $11$ than $7$ is, the average shifts upward.

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