How much exactly is increased when it is "increased by 1.1"?

Solution 1:

The sentence really should have read:

Unfortunately, it increases the CPI by a factor of 1.1.

One would probably not find this sort of ambiguity in a math text, but it is certain that a factor of was implied.

Note, however, that

Unfortunately, it increases the CPI to 1.1

does not mean the same thing! This implies, the final value of the CPI, after the increase, is 1.1.

by is used to indicate a product, but usually in an explicit manner, e.g.

• Taxes increased by 10%.
• Multiply your answer by 3.
• The new energy rating has decreased, by a factor of 1.5.

Indeed, in the absence of any context, I could be tempted to take

Unfortunately, it increases the CPI by 1.1

to mean 1.1 is added to the CPI, but I would really hard-pressed to do that! In a mathematical context, though, when one sees by, one should begin to think multiplication or division.

Solution 2:

X increased by 1.1 → X is now 1.1 times the previous value of X (10% increase)

X increased to 1.1 → X is now 1.1 (before it was less than 1.1)

Note that this is my interpretation of increased by in this particular context. In general, however, I would interpret increased by as an addition, i.e. 1.1 added to the original value.