Compare Averages: Determining if 12,16 = 10,20,25,5,10

Calculate the average of each group and choose the appropriate sign (?):

12,16=?10,20,25,5,10 12,16\stackrel{?}{=}10,20,25,5,10

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Step-by-step video solution

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00:00 Calculate the average of each group and choose the appropriate sign
00:05 To calculate the average, we need to divide the sum by the number of occurrences
00:23 This is the average, now let's use the same method for the second group
01:11 Let's compare and match the sign
01:15 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Calculate the average of each group and choose the appropriate sign (?):

12,16=?10,20,25,5,10 12,16\stackrel{?}{=}10,20,25,5,10

2

Step-by-step solution

To solve this problem, we'll determine the average of both groups and compare the results:

  • Step 1: Calculate the average of the first group (12,16)(12, 16).
    The sum of the first group is 12+16=28 12 + 16 = 28.
    There are 2 numbers, so the average is 282=14 \frac{28}{2} = 14.
  • Step 2: Calculate the average of the second group (10,20,25,5,10)(10, 20, 25, 5, 10).
    The sum of the second group is 10+20+25+5+10=70 10 + 20 + 25 + 5 + 10 = 70.
    There are 5 numbers, so the average is 705=14 \frac{70}{5} = 14.
  • Step 3: Compare the averages.
    Both groups have an average of 14; thus, the correct sign is = = .

Since both averages are equal, the conclusion is that the groups have the same average.
Therefore, the solution to the problem is =.

3

Final Answer

=

Practice Quiz

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

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