Ohio Assessments for Educators (OAE) Mathematics Practice Exam

Which of the following formulas represents standard deviation?

1. (Σ(x - mean))/n

2. (Σ(x - mean)²)/n

3. (Σ(mean - x)²)/n

4. √(Σ(x - mean)²)/n

The correct answer is: √(Σ(x - mean)²)/n

The formula for standard deviation is essentially a measure of how spread out the values in a data set are around the mean. To find the standard deviation, you first calculate the variance, which is the average of the squared differences from the mean. In this case, the correct option describes the complete process for calculating standard deviation. The formula involves: 1. **Finding the mean** of the data set. 2. **Calculating the squared differences** from the mean for each data point, which is represented as \( Σ(x - \text{mean})² \). This part measures how much each data point deviates from the mean. 3. **Averaging those squared differences** by dividing by \( n \), which is the number of data points, to get the variance. 4. Finally, taking the **square root** of that average (variance) to find the standard deviation itself. This step is critical because standard deviation is in the same unit as the original data, while variance is in squared units. Thus, the correct answer reflects all these steps accurately: you are summing the squared deviations from the mean, averaging that sum, and then taking the square root to arrive at the standard deviation.