Compare Averages: Determine if 30,30,30 Equals 30,30,30,30,30

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

30,30,30=?30,30,30,30,30 30,30,30\stackrel{?}{=}30,30,30,30,30

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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
00:30 Let's compare and match the sign
00:34 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 (?):

30,30,30=?30,30,30,30,30 30,30,30\stackrel{?}{=}30,30,30,30,30

2

Step-by-step solution

To solve this problem, follow these steps:

  • Step 1: Calculate the average for the first group of numbers: 30, 30, 30.
  • Step 2: Calculate the average for the second group of numbers: 30, 30, 30, 30, 30, 30.
  • Step 3: Compare the two averages using the appropriate sign.

Now, let's calculate each step:

Step 1: The first group is 30, 30, 30.
The sum is 30+30+30=9030 + 30 + 30 = 90.
The count is 3.
The average is 903=30\frac{90}{3} = 30.

Step 2: The second group is 30, 30, 30, 30, 30, 30.
The sum is 30+30+30+30+30+30=18030 + 30 + 30 + 30 + 30 + 30 = 180.
The count is 6.
The average is 1806=30\frac{180}{6} = 30.

Step 3: Compare the averages:
First average = 30 and Second average = 30. Thus, they are equal.

Therefore, the appropriate mathematical sign between the two groups is =\boxed{=}.

3

Final Answer

=

Practice Quiz

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

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