if i have a data set that overall is symmetric and i add a data point that is very low, what will happen to…

if i have a data set that overall is symmetric and i add a data point that is very low, what will happen to the mean?\nthe mean will decrease.\nthe mean will increase.\nthe mean will be raised by one data point value.\nthe mean will not change unless that data point was already in the data set.

if i have a data set that overall is symmetric and i add a data point that is very low, what will happen to the mean?\nthe mean will decrease.\nthe mean will increase.\nthe mean will be raised by one data point value.\nthe 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 low data - point

Let the original sum of data - points be $S=\sum_{i = 1}^{n}x_{i}$ and the original mean be $\bar{x}1=\frac{S}{n}$. After adding a new data - point $x{new}$ (where $x_{new}$ is very low), the new sum is $S'=S + x_{new}$ and the new number of data - points is $n'=n + 1$. The new mean $\bar{x}2=\frac{S + x{new}}{n + 1}$. Since $x_{new}$ is very low, it will pull the sum down, and when divided by $n + 1$, the new mean will be less than the original mean.

Answer:

The mean will decrease.