Question

which value can be added to the set below without changing its mean?
{4, 10, 14, 18, 22, 22}
○ 0
○ 15
○ 16
○ 22

Explanation:

Step1: Calculate the mean of the original set

First, find the sum of the numbers in the set \(\{4, 10, 14, 18, 22, 22\}\). The sum \(S = 4 + 10 + 14 + 18 + 22 + 22\). Let's calculate that: \(4+10 = 14\), \(14+14 = 28\), \(28+18 = 46\), \(46+22 = 68\), \(68+22 = 90\). There are 6 numbers, so the mean \(\mu=\frac{90}{6}=15\).

Step2: Determine the value to add

To not change the mean when adding a new number \(x\), the new mean (with 7 numbers) should also be 15. The new sum will be \(90 + x\), and the number of elements is \(7\). So we set up the equation \(\frac{90 + x}{7}=15\). Multiply both sides by 7: \(90 + x = 105\). Subtract 90 from both sides: \(x = 15\). So adding 15 will keep the mean the same.

Answer:

15