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 original mean

The sum of the numbers in the set $\{4, 10, 14, 18, 22, 22\}$ is $4 + 10+14 + 18+22+22=90$. There are $n = 6$ numbers. The mean $\bar{x}_1=\frac{90}{6}=15$.

Step2: Let the new - added number be $x$.

The new set will have $n_2=7$ numbers. We want the new mean $\bar{x}_2$ to be equal to the original mean. So, $\bar{x}_2=\frac{90 + x}{7}=15$.

Step3: Solve for $x$.

Multiply both sides of the equation $\frac{90 + x}{7}=15$ by $7$: $90 + x=105$. Then subtract $90$ from both sides: $x=105 - 90=15$.

Answer:

15