which value can be added to the set below without changing its mean? {4, 10, 14, 18, 22, 22} 0 15 16 22
which value can be added to the set below without changing its mean? {4, 10, 14, 18, 22, 22} 0 15 16 22
Answer
Explanation:
Step1: Calculate the original mean
The mean of a set of numbers ${x_1,x_2,\cdots,x_n}$ is $\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}$. For the set ${4, 10, 14, 18, 22, 22}$, $n = 6$ and $\sum_{i=1}^{6}x_i=4 + 10+14 + 18+22+22=90$. The mean $\bar{x}=\frac{90}{6}=15$.
Step2: Let the new - added number be $x$.
The new set has $n'=7$ elements, and we want the new mean to be the same as the original mean. So, $\frac{90 + x}{7}=15$.
Step3: Solve the equation 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:
B. 15