SAS input to be used for chi squared goodness of fit

#1
i have a data set I need to enter into SAS so I can perform a chi squared goodness-of-fit. The categories being used are <=12.9, >12.9 and <=13.9, >13.9 and <=14.9, and >14.9

I've referenced two of my books and in one, the data is entered as seen on the left and in another as seen on the right (see attached screen shot.).

To me, the categories above translate to non-overlapping buckets. So I don't understand why one would enter the data as shown on the right.

One classmate said the version on the right is how you adjust for continuity in SAS. Is that a correct statement?. The example the professor used in class (for a different problem) also took the approach on the right; however, he made no mention of continuity adjustment. The current assignment asks that we DO NOT adjust for continuity, so does that mean I enter as on the left?

Needless to say, I get different chi-squared and p-values, so I want to ensure I take the right approach.