Two economists Mark Bils and Peter Klenow investigated the raw data for 350 detailed spending categories that are used to generate the consumer price index (CPI)

The flexible-price CPI is represented by the Blue solid line.

Explaination- The consumer price index shows the aggregate bundle price of goods and services in the economy, and in the question, it's been stated that we have to calculate the index price for 350 goods in the economy where half or 175 goods have flexible prices and half are sticky prices. It means that the prices of those 175 goods change every 4.3 months or less than that. Now it is clear that flexible prices change more frequently than sticky prices(as they can change many times a year but sticky prices can change only a maximum of 2 times.

If we analyze the data carefully, both(blue solid and red dashed) indices are different in their fluctuation, that is the blue solid line fluctuates more on a yearly basis than the red dotted line. We only have to consider this point, that yearly fluctuation in the flexible prices are more. There were some instances where the red-dotted line showed a more steep ups and down as compared to the blue solid line but that will not be matter of concern as this can be due to high changes in large numbers of sticky prices goods than flexible prices goods.