Question

1. another college is asked and says students pay $15,000. what is the effect on the mean and standard deviation?

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Adding a new data - point $x_{new}$ changes the sum to $\sum_{i = 1}^{n}x_{i}+x_{new}$ and the number of data - points to $n + 1$. If the original mean is $\bar{x}$, the new mean $\bar{x}_{new}=\frac{n\bar{x}+x_{new}}{n + 1}$. If $x_{new}$ is greater than the original mean, the new mean will increase; if $x_{new}$ is less than the original mean, the new mean will decrease. Without knowing the original mean, we can't say exactly, but in general, the mean will change.

Step2: Recall standard - deviation formula

The standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$. Adding a new data - point $x_{new}$ changes the deviations of all data - points from the new mean and also adds a new deviation $(x_{new}-\bar{x}_{new})^{2}$. So the standard deviation will also change as the spread of the data set has been altered.

Answer:

The mean and the standard deviation will change.