The simple aggregate method totals the raw prices before comparing them, while the price-relatives method first converts each commodity's own change to a percentage and then averages those percentages — the two need not agree. …

1. Simple Aggregate Method:

   $P_{01} = \dfrac{\sum p_1}{\sum p_0}\times 100$

   $\sum p_0 = 10+20+30+40 = 100$; $\sum p_1 = 12+25+33+44 = 114$.

   $P_{01} = \dfrac{114}{100}\times 100 = 114$

2. Simple Average of Price Relatives Method. First compute each commodity's price relative $(p_1/p_0)\times 100$:

$P_{01} = \dfrac{\sum(\text{price relatives})}{n} = \dfrac{465}{4} = 116.25$ …

Averaging the raw prices instead of the price relatives in method (b); forgetting to multiply by 100 when computing a price relative or the final index; and assuming the two methods must give the same answer ( …