So I typed in 277 values from our sample and it came back with the mean is 14.015 and the standard deviation is 3.255. I am trying to figure the precise standard deviation we should have based on an exact distribution we would get without random chance. Of course, the Mean would be 14.000 so the fact this comes so close to that is probably as good as we could see.
I believe of the 1296 results we would get if we got every possible result one time we should get ...
4 ... 1 time
5 ... 4 times
6 ... 10 times
7 ... 20 times
and so on until
21 ... 20 times
22 ... 10 times
23 ... 4 times
24 ... one time
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Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
the median has as many values higher as it has values lower. It’s the 50% mark when you sort the set from lowest to highest. If the distribution of values is skewed, towards lower or higher values, the median-to-mean distance would be significant.
Yup. That's what I understood it to be as well. When rolling dice like we're going, it's going to be hard to see a median that is far away from the mean.
When I am checking Concrete Strength samples, you have an artificial lower bound, but there is no real upper bound, so the average and the median can be different values. In this dice roll challenge, we have a fixed top and bottom value so the skew would have to come from funny business. And the funny business would have to be pretty wild.
Happy New Year and Merry Christmas!
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13
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
4d6 = 19
So I typed in 277 values from our sample and it came back with the mean is 14.015 and the standard deviation is 3.255. I am trying to figure the precise standard deviation we should have based on an exact distribution we would get without random chance. Of course, the Mean would be 14.000 so the fact this comes so close to that is probably as good as we could see.
I believe of the 1296 results we would get if we got every possible result one time we should get ...
4 ... 1 time
5 ... 4 times
6 ... 10 times
7 ... 20 times
and so on until
21 ... 20 times
22 ... 10 times
23 ... 4 times
24 ... one time
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
A purple 19, quite a rare catch. Thanks for the summary. A mean to median comparison would shed some light on whether or not the ensemble is skewed.
13
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
9
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
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4d6 = 14
The median result was a 14, unless my recollection of median is off.
Yes, a purple 19 only happens as often as either a 5 or a 23; 4 : 1296.
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13
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
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4d6 = 12
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
15
the median has as many values higher as it has values lower. It’s the 50% mark when you sort the set from lowest to highest. If the distribution of values is skewed, towards lower or higher values, the median-to-mean distance would be significant.
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
11
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
14
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
8
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
8
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
16
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
9
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
4d6 = 16
Cyreon,
Yup. That's what I understood it to be as well. When rolling dice like we're going, it's going to be hard to see a median that is far away from the mean.
When I am checking Concrete Strength samples, you have an artificial lower bound, but there is no real upper bound, so the average and the median can be different values. In this dice roll challenge, we have a fixed top and bottom value so the skew would have to come from funny business. And the funny business would have to be pretty wild.
Happy New Year and Merry Christmas!
Cum catapultae proscriptae erunt tum soli proscript catapultas habebunt
17
Happy New Year to you, too. And a few more nice holidays!
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
16
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
We rolled the same numbers, MusicScout, but in different orders. How low are those odds?
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟
14
|| Oriace - Halfling Bard - Dragon Heist || Valerian - Elf Rogue - Wildnis || Rowan - Halfling Giant - Runewarren || Khazela - Spiritfarer Dervish - Yawning Portal || Arista - Frost Sorcerer - Old Keep || Marasatra - Blood Mage - Avernus || Lan Shi - Liquid Swords || Syed - Drakkenheim || Kaelthor - Dragonlance ||
13
⌜╔═════════════ The Board ══════════════╗⌝
...and started me on my way into my next chapter in life...
⌞╚════════════ Extended Signature ════════════╝⌟