Calculate Average: Compare {4,5,10,5,1,5} vs {4,5,10,5,1}

Q: Why do both groups have the same average when the sums are different?

The first group has sum 30 with 6 numbers, so average = $ \frac{30}{6} = 5 $. The second group has sum 25 with 5 numbers, so average = $ \frac{25}{5} = 5 $. Same average!

Q: What happens when I remove a number that equals the average?

When you remove a number that equals the current average (like removing the 5), the average stays the same! This is because removing an "average" value doesn't change the balance.

Q: How do I know which sign to use between the averages?

Calculate both averages completely first. Then compare the final decimal values: if left average > right average, use >; if left

Q: Can I just look at the numbers to guess the answer?

No! Always calculate the actual averages. Even though one group has more numbers, the averages might still be equal or the smaller group might have a higher average.

Q: What if I get different averages? How do I double-check?

Recount the elements in each groupRecalculate each sum carefullyDivide sum by count for each groupCompare the final decimal results

Average Comparison with Missing Elements

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

$4,5,10,5,1,5\stackrel{?}{=}4,5,10,5,1$

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Calculate the average of each group and choose the appropriate sign

00:06 To calculate the average, we need to divide the sum by the number of occurrences

00:22 We'll use the same method for the average in the second group

00:32 Now let's calculate each average and compare

01:32 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 each group and choose the appropriate sign (?):

$4,5,10,5,1,5\stackrel{?}{=}4,5,10,5,1$

Step-by-step solution

To solve this problem, let's calculate the average for each group of numbers:

Step 1: Calculate the average of the first group $4, 5, 10, 5, 1, 5$ :
- Sum of numbers: $4 + 5 + 10 + 5 + 1 + 5 = 30$
- Number of elements: $6$
- Average: $\frac{30}{6} = 5$
Step 2: Calculate the average of the second group $4, 5, 10, 5, 1$ :
- Sum of numbers: $4 + 5 + 10 + 5 + 1 = 25$
- Number of elements: $5$
- Average: $\frac{25}{5} = 5$

Both groups have an average of $5$ , so the correct sign to place between them is =.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Rule: Average equals sum divided by count of elements
Technique: Calculate sum: 4+5+10+5+1+5=30, then 30÷6=5
Check: Verify both averages match before comparing: 5=5 ✓

Common Mistakes

Avoid these frequent errors

Comparing sums instead of averages
Don't compare 30 vs 25 and conclude 30>25! This ignores the different counts (6 vs 5 elements). Always divide each sum by its count to find the true average before comparing.

Practice Quiz

Test your knowledge with interactive questions

If the balls below are divided so that each column in the table contains an equal number, then how many balls will there be in each column?

FAQ

Everything you need to know about this question

Why do both groups have the same average when the sums are different?

The first group has sum 30 with 6 numbers, so average = $\frac{30}{6} = 5$ . The second group has sum 25 with 5 numbers, so average = $\frac{25}{5} = 5$ . Same average!

What happens when I remove a number that equals the average?

When you remove a number that equals the current average (like removing the 5), the average stays the same! This is because removing an "average" value doesn't change the balance.

How do I know which sign to use between the averages?

Calculate both averages completely first. Then compare the final decimal values: if left average > right average, use >; if left < right, use <; if equal, use =.

Can I just look at the numbers to guess the answer?

No! Always calculate the actual averages. Even though one group has more numbers, the averages might still be equal or the smaller group might have a higher average.

What if I get different averages? How do I double-check?

Recount the elements in each group
Recalculate each sum carefully
Divide sum by count for each group
Compare the final decimal results

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Data Exploration questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime