Calculate the Mean: Finding Average of 3, 7, and 2 Toys per Box

Mean Calculation with Three Data Values

Below is a table describing the number of toys Jonathan has in his toy boxes.

Calculate the average number of toys in each box.

Toy BoxNumberofToys123372

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Step-by-step written solution

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1

Understand the problem

Below is a table describing the number of toys Jonathan has in his toy boxes.

Calculate the average number of toys in each box.

Toy BoxNumberofToys123372

2

Step-by-step solution

To solve this problem, we'll calculate the average number of toys in Jonathan's toy boxes using the following steps:

  • Step 1: Identify the total number of toys. Add up the quantities of toys from each box.
  • Step 2: Calculate the average by dividing the total number of toys by the number of boxes.

Let's perform the calculations:

Step 1: The number of toys in Box 1 is 3, in Box 2 is 7, and in Box 3 is 2. Therefore, the total number of toys is:

3+7+2=12 3 + 7 + 2 = 12

Step 2: There are 3 toy boxes. We calculate the average number of toys per box by dividing the total number of toys (12) by the number of boxes (3):

Average=123=4 \text{Average} = \frac{12}{3} = 4

Therefore, the average number of toys in each box is 4 4 .

3

Final Answer

4

Key Points to Remember

Essential concepts to master this topic
  • Definition: Mean equals sum of all values divided by count
  • Formula: Mean=3+7+23=123=4 \text{Mean} = \frac{3 + 7 + 2}{3} = \frac{12}{3} = 4
  • Check: Total toys (12) ÷ boxes (3) = 4 toys per box ✓

Common Mistakes

Avoid these frequent errors
  • Forgetting to count all the boxes when dividing
    Don't add up values like 3 + 7 + 2 = 12 and stop there = incomplete answer! Students often forget the division step entirely. Always divide your sum by the total number of data values (boxes) to get the mean.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

What's the difference between mean and total?

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The total is just adding up all values (3 + 7 + 2 = 12 toys), but the mean tells you the average per box by dividing that total by the number of boxes!

Why do we divide by 3 and not by 12?

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We divide by 3 because that's how many toy boxes there are! The mean formula is always: total ÷ number of items. Here we have 3 boxes, so we divide by 3.

What if the numbers don't divide evenly?

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That's totally normal! If you get a decimal or fraction, that's your answer. For example, if the total was 13 toys in 3 boxes, the mean would be 133=4.33... \frac{13}{3} = 4.33... toys per box.

How can I check if my mean is reasonable?

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Look at your original numbers! Your mean should be between the smallest and largest values. Since we have 2, 3, and 7, our mean of 4 makes sense because 2 < 4 < 7.

Does the order of the numbers matter when calculating mean?

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No! Whether you add 3 + 7 + 2 or 2 + 7 + 3 or any other order, you'll get the same sum (12) and the same mean (4). Addition is commutative!

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