Hi, I have a question regards to finding the real wages.

First, i can understand how to find the real wages with given nominal wages and

of course the given CPI index.

However, now my professor asks to find it via using PCE index,

"Personal Consumption Expenditures: Chain-type Price Index (PCEPI) | FRED |"

in which there is no way that i can get some hint out of it with googling.

so lets say,

May of 2016 nominal wage sets at $21.47, and

Jan of 2011 nominal wage sets at $19.32

now,

PCEI of may 2016 sets at 103.977

jan 2011 sets at 96.835

*note its different than what prof gave us

as i am just trying to understand

given this how can i find the real wage of may 2016, and jan 2011?

secondly, what makes the number of these two being different, and what would be the behind this

that differences in between finding the real wage with CPI and with PCEI

Thanks in advance.!