Q.Using the Laspeyres index (L = 127.59) and Paasche index (P = 127.41) already found in Examples 5 and 6, calculate Fisher's Ideal Price Index for the same data.

Fisher's Ideal Index is defined as the geometric mean of the Laspeyres and Paasche indices already computed. …

Step 1 — Apply Fisher's formula directly to the already-computed L and P.

Step 2 — Multiply and take the square root. …

Cross-check by computing F directly from the raw aggregates, without going through L and P. $F=\sqrt{\frac{\sum p_1q_0}{\sum p_0q_0}\times\frac{\sum p_1q_1}{\sum p_0q_1}}\times100=\sqrt{\frac{1110}{870}\times\frac{1018}{799}}\times100=\sqrt{1.2759\times1.2741}\times100\approx\sqrt{1.6260}\times100\approx127.51$ — matc …

Taking the plain ARITHMETIC mean, $(L+P)/2$, instead of the GEOMETRIC mean, $\sqrt{L\times P}$ — the two give very close values when L and P are themselves close (as here), which can mask the error, but Fisher's index is defined s …