RuneScape:Grand Exchange Market Watch/Adjustments (23 July 2013)

23 July 2013
Christmas cracker 31 December 2008 688,800,000 2,147,483,557 Unchanged
Blue partyhat 340,100,000 2,147,483,647
Green partyhat 114,800,000 1,845,813,270
Purple partyhat 83,100,000 1,514,338,96
Red partyhat 129,400,000 2,100,264,784
White partyhat 183,300,000 2,147,483,598
Yellow partyhat 96,300,000 1,607,195,89
Pumpkin 5,300,000 177,606,966
Easter egg 4,300,000 82,884,794
Santa hat 14,800,000 149,818,733
Disk of returning 4,700,000 226,927,013
Half full wine jug 31,100,000 320,604,356
Fish mask 29 September 2012 4,555,462 1,446,274
Christmas tree hat 20 January 2013 2,295,576 26,024,637
Crown of Seasons 8,307,542 Added item

Calculations

From the old divisor obtained from the templates:

${\displaystyle {div}_{\text{old}}=15.1547}$

We need to calculate a new divisor:

${\displaystyle {div}_{\text{new}}={div}_{\text{old}}\times {\frac {\sum \left({\frac {p}{q}}\right)_{\text{new}}}{\sum \left({\frac {p}{q}}\right)_{\text{old}}}}}$

To calculate the new divisor, we need to find:

{\displaystyle {\begin{aligned}\sum \left({\frac {p}{q}}\right)_{\text{old}}&={\text{sum of ratios prior to change}}\\&={\frac {2,147,483,557}{688,800,000}}+{\frac {2,147,483,647}{340,100,000}}+{\frac {1,845,813,270}{114,800,000}}+\dots +{\frac {26,024,637}{2,295,576}}\\&=260.57227963{\text{ (up to 8 d.p.)}}\end{aligned}}}

And also:

{\displaystyle {\begin{aligned}\sum \left({\frac {p}{q}}\right)_{\text{new}}&={\text{sum of ratios prior to change}}-{\text{sum of removed ratios}}+{\text{sum of added ratios}}\\&=\sum \left({\frac {p}{q}}\right)_{\text{old}}-{\text{sum of removed ratios}}+{\text{number of added items}}\\&=260.57227963-0+1\\&=261.57227963{\text{ (up to 8 d.p.)}}\end{aligned}}}

Thus, the new divisor is:

{\displaystyle {\begin{aligned}{div}_{\text{new}}&={div}_{\text{old}}\times {\frac {\sum \left({\frac {p}{q}}\right)_{\text{new}}}{\sum \left({\frac {p}{q}}\right)_{\text{old}}}}\\&=15.1547\times {\frac {261.57227963}{260.57227963}}\\&=15.2129{\text{ (4 d.p.)}}\end{aligned}}}