average of five numbers is 20. if each number is multiplied by 2, what will be the new average?
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Average of Five Numbers is 20 — What Happens if We Multiply Each by 2?
Quick Scoop
When we talk about averages, small manipulations can make a big difference. Let’s see how multiplying each number changes the overall average.
🧮 Step-by-Step Breakdown
Let the five numbers be a,b,c,d,a,b,c,d,a,b,c,d, and eee.
Step 1: Original Average
Given:
a+b+c+d+e5=20\frac{a+b+c+d+e}{5}=205a+b+c+d+e=20
That means the sum of the numbers is:
a+b+c+d+e=20×5=100a+b+c+d+e=20\times 5=100a+b+c+d+e=20×5=100
Step 2: Multiplying Each by 2
If each number is multiplied by 2, the new numbers become 2a,2b,2c,2d,2a,2b,2c,2d,2a,2b,2c,2d, and 2e2e2e. Their new sum will be:
2a+2b+2c+2d+2e=2×(a+b+c+d+e)=2×100=2002a+2b+2c+2d+2e=2\times (a+b+c+d+e)=2\times 100=2002a+2b+2c+2d+2e=2×(a+b+c+d+e)=2×100=200
Step 3: Finding the New Average
New average=2005=40\text{New average}=\frac{200}{5}=40New average=5200=40
✅ Final Answer: The new average is 40.
💡 Quick Concept
When every number in a data set is multiplied by the same constant, the
average also gets multiplied by that constant. Example:
If the original average was 20 and we double every number, the new average
becomes 20×2=40.20\times 2=40.20×2=40.
📈 Fun Perspective
Think of the average as the center weight of a balance. If you double each weight, the balance shifts to double the total — but the “shape” of the data pattern doesn’t change, just the scale.
🔢 Quick Recap in Table Form
| Action | Sum | Average |
|---|---|---|
| Original numbers | 100 | 20 |
| After multiplying each by 2 | 200 | 40 |
