Q.If $I_P = I_F$, which of the following statements is true?

$I_F=\sqrt{I_L I_P}$, so $I_P=I_F\Rightarrow I_F=I_P=I_L$.

Fisher's ideal index number is the geometric mean of the Laspeyres and Paasche indices:

$I_F=\sqrt{I_L\cdot I_P}.$

Squaring both sides: $I_F^2=I_L\cdot I_P$. Given $I_P=I_F$, substitute: …

The two popular methods of assigning explicit weight are Laspeyre's method (base-year quantity weights) and Paasche's method (current-year quantity weights).

While constructing a weighted index number, explicit weights (usually quantities) are attached to the prices. The two most widely used methods of assigning such explicit weights are:

1. Laspeyre's method — uses the base-year quantities $q_0$ as weights: $P_{01}=\dfrac{\sum p_1 q_0}{\sum p_0 q_0}\times100$. …