Hello, everyone - one of my students just emailed me asking about problem no. 104 from the Stats book, so I figured I'd share my response for anyone who might also be wondering...

QUESTION:

In the Stats book, q104 I don't understand the requirement. Adding the same number shouldn't have an impact on the standard deviation.

Sets A, B and C are evenly spaced. A has the most standard deviation, followed by B and C. I don't understand the explanation as to why E is correct...





MY RESPONSE:

Good question on this one - it really comes down to what they're specifically asking, as many of these questions do:

Which represents the correct ordering of the sets in terms of the ABSOLUTE INCREASE in their standard deviation?

They're asking - if you place the number 100 as an additional term in each of these sets, how will the presence of that extra term impact the standard deviation:

A) 30, 50, 70. 90, 100 (new), 110 ---> Doesn't change the standard deviation much...it fits within the range of the current set of numbers and only skews it a little bit.

B) -20, -10, 0, 10, 20, 100 (new) ---> This adds a pretty significant change to the standard deviation - the original average was 0, and now we add 100 to it which is far, far away from that. This may well be the biggest.

C) 30, 35, 40, 45, 50, 100 (new) ----> This also adds a pretty big change - 100 is pretty far from the initial average of 40.

It's somewhat tough to determine exactly how different the changes are in B and C - C has a smaller standard deviation to start, but is less impacted by the sheer volume of 100 (it's 60 away from the previous average, whereas in B it's 100 away). But if you look at the answers, E is the only one that has A as the smallest increase in Standard Deviation, so it's the only contender, and therefore the correct choice.