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

Video Solution

Solution Steps

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 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 $12$ .