## More Standard Deviation

Summary
This lesson delves into advanced topics on standard deviation, focusing on its implications when adding new members to a set, its role as a unit of measurement, and the intricacies of its calculation.
• Adding new members to a set can increase, decrease, or maintain the standard deviation, depending on how the new numbers compare to the mean.
• Standard deviation serves as a crucial unit of measurement, helping to contextualize individual scores within large sets or populations.
• The calculation of standard deviation involves a multi-step process, including finding the mean, calculating deviations, squaring these, and taking the square root of the average squared deviation.
• Understanding the impact of adding numbers to a set and the conceptual use of standard deviation as a measurement unit is essential for interpreting data sets effectively.
• While the GRE will not require detailed standard deviation calculations, grasping these concepts is vital for tackling advanced quantitative questions.
Chapters
00:00
Impact of Adding New Members to a Set
07:19
Standard Deviation as a Unit of Measurement
10:32
Calculating Standard Deviation

Related Blog Posts

Standard Deviation on the New GRE

a detailed GMAT blog: Standard Deviation

FAQ: What is the variance and how do we calculate it?

A: The variance is simply defined as the square of the standard deviation. So if the standard deviation is 5, the variance is 25.

In statistics, variance plays an important role in telling us how much we can expect a number to deviate from the mean. Imagine if the government were assessing the income level in a certain region to determine whether or not to provide aid. The average income of the region happens to match the overall average income so the government initially thinks the region is fine and they shouldn't provide aid. But upon closer inspection, it turns out there are a few very rich people in the region and then a vast majority of people spread below the average income line. There's a high variance from the mean and so the government should consider providing aid.

So for the purposes of the GRE, when discussing the deviation from the mean, you're pretty much guaranteed to only see standard deviation, as it's a more commonly used statistical measure of deviation. However, if you're asked about variance, it will be explicitly stated. I've never even seen a scenario where you're expected to calculate the variance based on the standard deviation, just to know that it measures deviation in a manner similar to standard deviation. So ultimately, it's not something you should worry about :)

FAQ: I've seen the actual equation for calculating standard deviation, and it scares me! How will I apply this on the GRE? Do I need to use that equation?

A: First, Chris wrote a great article that discusses when, where, and how standard deviation questions are on the exam:

The most important thing that most SD questions will test is your understanding of the concept of how SD is calculated and what it is, and combine that with your overall understanding of number sense and statistics. You can see in both of Chris's examples that the key is understanding what SD is all about. If you can do that, the calculations themselves are pretty straightforward :D