Calculate the Average of 7, 6, 5, 5: Step-by-Step Solution

Q: Why do I count the number 5 twice if it's the same value?

Each position in your data set counts as one number, even if the values are identical! You have four separate data points: 7, 6, 5, and 5.

Q: Can I leave my answer as a decimal instead?

Yes! 5.75 and $ 5\frac{3}{4} $ are the same value. Choose the form that matches what your question asks for or what seems clearest.

Q: What if I get the sum wrong at the beginning?

Double-check your addition: 7+6=13, then 13+5=18, finally 18+5=23. One small error in the sum makes your entire average incorrect!

Q: Is there a faster way to check if my average is reasonable?

Your average should be between your smallest and largest values (5 and 7)Since you have two 5s, the average should be closer to 5 than to 7$ 5\frac{3}{4} $ fits perfectly!

Average Calculation with Mixed Number Result

Calculate the average

of $7,6,5,$ and $5$ .

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the average

00:03 To calculate the average, we need to divide the sum by the number of occurrences

00:07 Let's sum up the numbers

00:12 And divide by the number of occurrences (4)

00:32 Let's break down 24 into 20 plus 3

00:41 Let's break it down into whole number and remainder

00:48 Convert from whole fraction to whole number

00:52 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

Calculate the average

of $7,6,5,$ and $5$ .

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Calculate the sum of the numbers.
Step 2: Determine the count of the numbers.
Step 3: Use the formula for the average.

Now, let's work through each step:
Step 1: Sum of the numbers = $7 + 6 + 5 + 5 = 23$ .
Step 2: Count of the numbers = 4.
Step 3: Apply the average formula:
$\text{Average} = \frac{23}{4} = 5.75$ This can be expressed as a mixed number, $5\frac{3}{4}$ .

Therefore, the average of 7, 6, 5, and 5 is $5\frac{3}{4}$ .

Final Answer

$5\frac{3}{4}$

Key Points to Remember

Essential concepts to master this topic

Formula: Average equals sum of values divided by count
Technique: Sum 7+6+5+5=23, then divide 23÷4=5.75
Check: Convert decimal 5.75 to mixed number $5\frac{3}{4}$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to count all numbers correctly
Don't count 7,6,5,5 as only 3 numbers because 5 appears twice = wrong average of 23÷3=7.67! Each value counts separately even if repeated. Always count every single number in your list.

Practice Quiz

Test your knowledge with interactive questions

Calculate the average of $$ 10 $$ and $$ 12 $$ .

FAQ

Everything you need to know about this question

Why do I count the number 5 twice if it's the same value?

Each position in your data set counts as one number, even if the values are identical! You have four separate data points: 7, 6, 5, and 5.

How do I convert 5.75 to a mixed number?

Take the whole number part (5) and convert the decimal part: 0.75 = $\frac{3}{4}$ . So 5.75 = $5\frac{3}{4}$ .

Can I leave my answer as a decimal instead?

Yes! 5.75 and $5\frac{3}{4}$ are the same value. Choose the form that matches what your question asks for or what seems clearest.

What if I get the sum wrong at the beginning?

Double-check your addition: 7+6=13, then 13+5=18, finally 18+5=23. One small error in the sum makes your entire average incorrect!

Is there a faster way to check if my average is reasonable?

Your average should be between your smallest and largest values (5 and 7)
Since you have two 5s, the average should be closer to 5 than to 7
$5\frac{3}{4}$ fits perfectly!

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