Question

suppose you have a data set that includes the values 20, 30, and 50. if you add a fourth value to this data set, and after doing that the mean of the data set is 50, what was the value that you added? a. -10 c. 50 b. 40 d. 100 please select the best answer from the choices provided

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n$ is the number of data - points and $\sum_{i = 1}^{n}x_{i}$ is the sum of the data - points. Initially, we have three data - points $20$, $30$, and $50$, and then we add a fourth value $x$. After adding the fourth value, $n = 4$ and $\bar{x}=50$.

Step2: Calculate the sum of the four data - points

We know that $\bar{x}=\frac{20 + 30+50 + x}{4}=50$. First, simplify the numerator of the left - hand side: $20+30 + 50+x=100 + x$. So the equation becomes $\frac{100 + x}{4}=50$.

Step3: Solve the equation for $x$

Multiply both sides of the equation $\frac{100 + x}{4}=50$ by $4$: $100 + x=200$. Then subtract $100$ from both sides: $x=200 - 100=100$.

Answer:

D. 100