# My Collection

**URL:** <https://forums.yoyoexpert.com/t/my-collection/307299>\
**Category:** Display Case\
**Created:** [August 23, 2019, 5:30pm UTC](https://forums.yoyoexpert.com/t/my-collection/307299 "2019-08-23T17:30:17Z")\
**Posts on this page:** 1\
**Showing post:** 9

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**Author:** ![threebearrries](https://sea1.discourse-cdn.com/flex015/user_avatar/forums.yoyoexpert.com/threebearrries/32/42073_2.png) [@threebearrries](https://forums.yoyoexpert.com/u/threebearrries)\
**Post date:** [August 24, 2019, 1:27am UTC](https://forums.yoyoexpert.com/t/my-collection/307299/9 "2019-08-24T01:27:01Z")

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You get what you ask for 🙂

OKAY let’s do the math

Problem: I’m claiming that the Ti-Vayder is

> [@Another $180 titanium yoyo pre-order](https://forums.yoyoexpert.com/t/another-180-titanium-yoyo-pre-order/299310/133):
>
> much too undersized to be enjoyable to me

So what does that really mean? Well, yoyos feel small when they have either a small diameter or a small width, so basically, a yoyo feels small when it doesn’t take up much space in your hand. We can quantify a yoyo’s ability to take up space with volume. To do this, we’ll need to simplify a yoyo’s dimensions to just its diameter and width, which, when simplified, leaves us with a nice cylinder for calculations. What I plan to do is create cylinders for all the yoyos in my collection and compare the Ti-Vayder’s cylinder to my collection’s cylinders.

Math:  
To quantify the difference between my collection and the Ti-Vayder, I’ll calculate the mean and standard deviation of the volumes of all my collection’s cylinders and then see how many standard deviations away the Ti-Vayder’s volume is (essentially how different the numbers are).

 ![image](https://us1.discourse-cdn.com/flex015/uploads/yoyoexpert1/original/4X/6/a/3/6a38bf712cb8fbc773ece522ea6e2620959c3411.png)  
 ![image](https://us1.discourse-cdn.com/flex015/uploads/yoyoexpert1/original/4X/7/a/0/7a05ea7d0e50b6d8337045167ff72732773ef02e.png)

Results (from above):  
Mean: 434 cm3  
Standard Deviation: 25 cm3  
Z-Score: -2.21

The results show that the average volume of the yoyo cylinders in my collection is 434 cm3. The Ti-Vayder’s volume is 378 cm3, a whopping 2.21 standard deviations away, which means that the probability of the Ti-Vayder belonging in my current collection is next to 0 (the second picture shows a graph of this likelihood). It’s quite interesting that the Ti-Vayder’s volume is only 12.7% less than the average volume of my collection, as it shows how much a few millimeters matter.

TL;DR: I did the math. The Ti-Vayder _is_ that much smaller than the rest of my collection.

Note: I know this is a pretty inadequate report from a statistics standpoint, I just didn’t want to do all of the proper analysis and explain every little thing lol ALSO I didn’t even conclude if the size of the Ti-Vayder is definitively not enjoyable for me, mainly bc the statistics done answer a completely different question. I think I would need to try a bunch of different yoyos near the lower volume of my collection and somehow determine the threshold for an unappealing volume.

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