UGA Math Placement Practice Exam – Free Practice Test & Study Guide

To find the standard deviation of the data set: 3, 7, 7, 19, it's important to follow these steps:

1. **Calculate the Mean**:

First, find the mean (average) of the data set. You do this by adding all the values and dividing by the number of values.

\[

\text{Mean} = \frac{3 + 7 + 7 + 19}{4} = \frac{36}{4} = 9

\]

2. **Calculate the Variance**:

Next, calculate the variance, which involves finding the squared differences from the mean, summing those, and then dividing by the number of values.

- For each value, subtract the mean and square the result:

- \((3 - 9)^2 = (-6)^2 = 36\)

- \((7 - 9)^2 = (-2)^2 = 4\)

- \((7 - 9)^2 = (-2)^2 = 4\)

- \((19 - 9)^2 = (10)^2 = 100\)

- Sum these squared differences: