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 current mean

Let the set be \(S=\{4, 10, 14, 18, 22, 22\}\). The number of elements \(n = 6\). The sum of elements \(sum=\sum_{i = 1}^{6}x_{i}=4 + 10+14 + 18+22+22=90\). The mean \(\bar{x}=\frac{sum}{n}=\frac{90}{6}=15\).

Step2: Let the new - element be \(x\).

The new number of elements is \(n'=7\), and we want the new mean \(\bar{x}'\) to be equal to the old mean. The new sum of elements is \(sum'=90 + x\). Since \(\bar{x}'=\frac{90 + x}{7}=15\).

Step3: Solve the equation for \(x\).

Cross - multiply the equation \(\frac{90 + x}{7}=15\) to get \(90+x = 15\times7=105\). Then \(x=105 - 90=15\).

Answer:

15