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 a b c d

Explanation:

Step1: Recall the formula for the mean

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. Here, $n = 4$ and $\bar{x}=50$. So, $\sum_{i = 1}^{4}x_{i}=n\times\bar{x}=4\times50 = 200$.

Step2: Find the sum of the known values

The sum of the known values is $20 + 30+50=100$.

Step3: Let the unknown value be $x$

We know that $20 + 30+50+x=200$. Substitute the sum of the known values: $100+x = 200$.

Step4: Solve for $x$

Subtract 100 from both sides of the equation: $x=200 - 100$.

Answer:

D. 100