## FANDOM

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The Discontinued Rare Index is made up of a weighted average of all of the discontinued rare items listed in the Market Watch, with the starting date of this average on 31 December 2008, at an index of 100. The overall rising and falling of discontinued rare item prices is reflected in this index.

While specialised for just watching discontinued rare item prices, it is set up and adjusted in a manner similar to the Common Trade Index, and the divisor may be adjusted to include new rare items "discontinued" by Jagex (see the FAQ for more information).

## Summary

Any suggested changes to this index should be added to the talk page.

## List of items

This is the current list of rare items included in this index:

29 September 2012
Christmas cracker 31 December 2008 688,800,000 2,146,908,554 Unchanged
Blue partyhat 340,100,000 2,147,483,647
Green partyhat 114,800,000 1,124,859,082
Purple partyhat 83,100,000 895,254,988
Red partyhat 129,400,000 1,232,179,013
White partyhat 183,300,000 1,652,939,303
Yellow partyhat 96,300,000 948,567,763
Pumpkin 5,300,000 165,935,075
Easter egg 4,300,000 56,837,419
Santa hat 14,800,000 116,884,816
Disk of returning 4,700,000 171,076,782
Half full wine jug 31,100,000 261,000,577

Calculations

From the old divisor obtained from the templates:

${div}_{\text{old}} = 15.0000$

We need to calculate a new divisor:

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

To calculate the new divisor, we need to find:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{2,146,908,554}{688,800,000} + \frac{2,147,483,647}{340,100,000} + \frac{1,124,859,082}{114,800,000} + \dots + \frac{261,000,577}{31,100,000} \\ & = 181.52107486 \text{ (up to 8 d.p.)} \end{align}

And also:

\begin{align} \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} \\ & = 181.52107486 - 0 + 1 \\ & = 182.52107486 \text{ (up to 8 d.p.)} \end{align}

Thus, the new divisor is:

\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 15.0000 \times \frac{182.52107486}{181.52107486} \\ & = 15.0826 \text{ (4 d.p.)} \end{align}
20 January 2013
Christmas cracker 31 December 2008 688,800,000 2,147,476,523 Unchanged
Blue partyhat 340,100,000 2,147,483,647
Green partyhat 114,800,000 1,439,919,758
Purple partyhat 83,100,000 1,194,593,128
Red partyhat 129,400,000 1,588,813,583
White partyhat 183,300,000 2,115,586,339
Yellow partyhat 96,300,000 1,288,308,900
Pumpkin 5,300,000 153,543,323
Easter egg 4,300,000 73,851,614
Santa hat 14,800,000 130,038,816
Disk of returning 4,700,000 193,631,082
Half full wine jug 31,100,000 282,814,298
Fish mask 29 September 2012 4,555,462 1,778,504
Christmas tree hat 2,295,576 Added item

Calculations

From the old divisor obtained from the templates:

${div}_{\text{old}} = 15.0826$

We need to calculate a new divisor:

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

To calculate the new divisor, we need to find:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{2,146,908,554}{688,800,000} + \frac{2,147,483,647}{340,100,000} + \frac{1,439,919,758}{114,800,000} + \dots + \frac{1,778,504}{4,555,462} \\ & = 209.14534690 \text{ (up to 8 d.p.)} \end{align}

And also:

\begin{align} \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} \\ & = 209.14534690 - 0 + 1 \\ & = 210.14534690 \text{ (up to 8 d.p.)} \end{align}

Thus, the new divisor is:

\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 15.0826 \times \frac{210.14534690}{209.14534690} \\ & = 15.1547 \text{ (4 d.p.)} \end{align}
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:

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

We need to calculate a new divisor:

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

To calculate the new divisor, we need to find:

\begin{align} \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{align}

And also:

\begin{align} \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{align}

Thus, the new divisor is:

\begin{align} {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{align}
20 January 2014
Christmas cracker 31 December 2008 688,800,000 2,147,483,632 Unchanged
Blue partyhat 340,100,000 2,147,483,647
Green partyhat 114,800,000 1,490,829,327
Purple partyhat 83,100,000 1,279,369,134
Red partyhat 129,400,000 1,696,893,747
White partyhat 183,300,000 2,146,833,194
Yellow partyhat 96,300,000 1,335,202,311
Pumpkin 5,300,000 174,290,712
Easter egg 4,300,000 70,272,905
Santa hat 14,800,000 135,913,306
Disk of returning 4,700,000 223,384,911
Half full wine jug 31,100,000 333,709,743
Fish mask 29 September 2012 4,555,462 944,822
Christmas tree hat 20 January 2013 2,295,576 12,593,302
Crown of Seasons 23 July 2013 8,307,542 3,926,892
Black Santa hat 222,967,707 Added item

Calculations

From the old divisor obtained from the templates:

${div}_{\text{old}} = 15.2129$

We need to calculate a new divisor:

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

To calculate the new divisor, we need to find:

\begin{align} \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{1,490,829,327}{114,800,000} + \dots + \frac{12,593,302}{2,295,576} + \frac{3,926,892}{8,307,542} \\ & = 230.87579845 \text{ (up to 8 d.p.)} \end{align}

And also:

\begin{align} \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} \\ & = 230.87579845 - 0 + 1 \\ & = 231.87579845 \text{ (up to 8 d.p.)} \end{align}

Thus, the new divisor is:

\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 15.2129 \times \frac{231.87579845}{230.87579845} \\ & = 15.2787 \text{ (4 d.p.)} \end{align}
19 June 2014
Christmas cracker 31 December 2008 688,800,000 2,147,483,644 Unchanged
Blue partyhat 340,100,000 2,147,483,647
Green partyhat 114,800,000 1,512,978,741
Purple partyhat 83,100,000 1,242,748,792
Red partyhat 129,400,000 1,706,390,538
White partyhat 183,300,000 2,147,481,758
Yellow partyhat 96,300,000 1,325,097,236
Pumpkin 5,300,000 157,608,053
Easter egg 4,300,000 62,666,643
Santa hat 14,800,000 125,533,632
Disk of returning 4,700,000 211,466,440
Half full wine jug 31,100,000 348,603,157
Fish mask 29 September 2012 4,555,462 669,574
Christmas tree hat 20 January 2013 2,295,576 12,559,556
Crown of Seasons 23 July 2013 8,307,542 4,555,009
Black Santa hat 20 January 2013 222,967,707 410,924,805
Cloak of Seasons 7,614,236 Added item

Calculations

From the old divisor obtained from the templates:

${div}_{\text{old}} = 15.2787$

We need to calculate a new divisor:

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

To calculate the new divisor, we need to find:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{2,147,483,644}{688,800,000} + \frac{2,147,483,647}{340,100,000} + \frac{1,512,978,741}{114,800,000} + \dots + \frac{4,555,009}{8,307,542} + \frac{410,924,805}{222,967,707} \\ & = 221.84047459 \text{ (up to 8 d.p.)} \end{align}

And also:

\begin{align} \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} \\ & = 221.84047459 - 0 + 1 \\ & = 222.84047459 \text{ (up to 8 d.p.)} \end{align}

Thus, the new divisor is:

\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 15.2787 \times \frac{222.84047459}{221.84047459} \\ & = 15.3476 \text{ (4 d.p.)} \end{align}
30 December 2014
Christmas cracker 31 December 2008 688,800,000 2,147,483,644 Unchanged
Blue partyhat 340,100,000 2,147,483,647
Green partyhat 114,800,000 1,452,340,733
Purple partyhat 83,100,000 1,233,390,908
Red partyhat 129,400,000 1,738,594,833
White partyhat 183,300,000 2,147,483,644
Yellow partyhat 96,300,000 1,314,553,072
Pumpkin 5,300,000 149,804,919
Easter egg 4,300,000 49,183,614
Santa hat 14,800,000 115,823,577
Disk of returning 4,700,000 200,971,362
Half full wine jug 31,100,000 348,603,157
Fish mask 29 September 2012 4,555,462 601,926
Christmas tree hat 20 January 2013 2,295,576 12,651,188
Crown of Seasons 23 July 2013 8,307,542 4,044,842
Black Santa hat 20 January 2013 222,967,707 340,890,058
Cloak of Seasons 19 June 2014 7,614,236 27,631,528
Off-hand rubber turkey 3,590,829
Christmas scythe 72,191,580
Holly wreath 372,492,991

Calculations

From the old divisor obtained from the templates:

${div}_{\text{old}} = 15.3476$

We need to calculate a new divisor:

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

To calculate the new divisor, we need to find:

\begin{align} \sum \left ( \frac{p}{q} \right )_{\text{old}} & = \text{sum of ratios prior to change} \\ & = \frac{2,147,483,644}{688,800,000} + \frac{2,147,483,647}{340,100,000} + \frac{1,452,340,733}{114,800,000} + \dots + \frac{340,890,058}{222,967,707} + \frac{27,631,528}{7,614,236} \\ & = 211.91329563 \text{ (up to 8 d.p.)} \end{align}

And also:

\begin{align} \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} \\ & = 211.91329563 - 0 + 4 \\ & = 215.91329563 \text{ (up to 8 d.p.)} \end{align}

Thus, the new divisor is:

\begin{align} {div}_{\text{new}} & = {div}_{\text{old}} \times \frac{\sum \left ( \frac{p}{q} \right )_{\text{new}}}{\sum \left ( \frac{p}{q} \right )_{\text{old}}} \\ & = 15.3476 \times \frac{215.91329563}{211.91329563} \\ & = 15.6373 \text{ (4 d.p.)} \end{align}
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