Question
Open Ended Make a data set that has 5 numbers and a balance poin
of 12 .
of 12 .
Ask by Hamilton Greene. in the United States
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A data set with 5 numbers that has a balance point (mean) of 12 is {10, 11, 12, 13, 14}.
Solution
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We interpret the “balance point” as the arithmetic mean, so for a data set with 5 numbers, the mean should be 12.
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The arithmetic mean is given bySetting the mean equal to 12 gives
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Multiply both sides by 5 to find the total sum needed:
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We now need to choose 5 numbers that add up to 60. One simple data set isVerify the sum:
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Since the sum is 60, the arithmetic mean (balance point) is
Thus, the data set
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Simplify this solution Beyond the Answer
To create a dataset with five numbers where the balance point (mean) is 12, we can start by constructing the equation for the mean:
( x₁ + x₂ + x₃ + x₄ + x₅ ) / 5 = 12.
Multiplying through by 5 gives us: x₁ + x₂ + x₃ + x₄ + x₅ = 60.
One possible dataset could be: 8, 12, 15, 10, and 15. Adding these numbers together results in 60, which means their mean is indeed 12.
Now, let’s have some fun with experimentation! You could swap some numbers out—like replacing 8 with 7 and adjusting another number slightly to keep the balance point at 12. For example, switch 15 to 16 to maintain the sum of 60: 7, 12, 16, 10, and 15. See how many combinations you can come up with that still balance out to that perfectly average number!
