if i have a data set that overall is symmetric and i add a data point that is very high, what will happen to…
if i have a data set that overall is symmetric and i add a data point that is very high, what will happen to the mean?\na the mean will decrease.\nb the mean will increase.\nc the mean will be raised by one data point value.\nd the mean will not change unless that data point was already in the data set.
Answer
Explanation:
Step1: Recall mean formula
The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are data - points and $n$ is the number of data - points.
Step2: Analyze effect of new high data point
Let the original sum of data points be $S=\sum_{i = 1}^{n}x_{i}$ and the original mean be $\bar{x}=\frac{S}{n}$. When we add a new data point $x_{new}$ (where $x_{new}$ is very high), the new sum is $S'=S + x_{new}$ and the new number of data points is $n'=n + 1$. The new mean $\bar{x}'=\frac{S + x_{new}}{n + 1}$. Since $x_{new}$ is very high, the value of $\bar{x}'$ will be greater than $\bar{x}$.
Answer:
B. The mean will increase.