Given the two data sets below, what is the relationship between the standard deviation of data set A and the standard deviation of data set B?
Data set A {109, 110, 110, 110, 111, 118, 118}
Data set B {3, 7, 9, 11, 52}
The correct answer is (A).
current priority level - we all want this one
Maybe we are being a touch ambitious with the current priority level here, but we don’t think so. We can all smash this one, so we all want this one.
As is so regularly the case with Math questions within this test, we have options here, and we are going to explore two of them.
We start with the desmos route, as via the “funcs” key, desmos can do the lifting for us here. Clicking on the “funcs” key, we then scroll down a bit to find the “stdev” button. Clicking on that button, we can then input the numbers that comprise data set A. Doing so, desmos computes for us a standard deviation of 3.9460649477. Repeating this process for data set B, desmos shows us that it has a standard deviation of 20.1196421439, leading us to being confident in selecting (A) as our correct answer.
Before we get to route two, let’s acknowledge two things…
So, as you can see, standard deviation is not tied to the size of given numbers or the quantity. What is not a coincidence is that data set A has a smaller range than data set B. The range of data set A is 9(118 - 109) and the range of data set B is 49(52 - 3). It is a thing that range and standard deviation correlate.
Let’s close out with two comments….