Construct the price index for a “fruit basket” in each year using $2003$as the base year.

A price index indicates changes in the price level of commodities in the current period as compared to the base year.

If $2003$is the base year then the index value of $2003$is $100$.

The total amount spent for $2003$is,

Amount spent each year = Quantity of each fruit*price.

That is $\$8.5,\$3.0,\$1.8,\$2.05$of Apple, banana, grapes, raspberries respectively.

By adding all the values we will get $\$15.35$,

Similarly for years $2001,2002,$and $2004$is $\$10.70,\$13.8$and$\$16.31$respectively.

The formula of the price index is,

Price index $=Priceofbasketforeachyear÷(Priceofbasketatbaseyear\times 100)$

Taking $2003$as the base year & we divide each year's value by $\$15.35$.

By putting the values in the formula, we will get the price index

$$\begin{gathered} 2001-69.71 \\ 2002-89.90 \\ 2003-100 \\ 2004-106.3 \end{gathered}$$