How would I find the most common value every nth row in a column

Question

SCENARIO 1
I have a column with a series of numbers in c1:c1000 as follows:
2
2
3
1
1
4
2
3
1
2...
and I would like to find the most common value for every nth (in this case, second) row.
SCENARIO 2
Originally, I created a separate column in J and used this to find a value of 0 or 1 via a filter to label the rows odd or even. I was then going to create two separate columns, one for even rows of data and another for odd rows of data to separate them and perform functions on each column. But I do not know how to copy just the filtered data to one of the new columns to apply the MODE function (or any other for that matter).
Perhaps my question should be: after applying a filter, how do i copy just the visible filtered data of every nth row to a new column in my spreadsheet while retaining the original column with all rows of data? 
BACK TO SCENARIO 1
If I do not need to go through this effort, I would just apply the MODE function (or AVERAGE or SUM) to every nth row in the original data column.

Answer 1

Since Index and Offset were already taken, I used INDIRECT(ADDRESS()) in my example.
Here's how I approached it:
Expressions are as follows...
Data Subset, Column A, Row 2: =IF(StartingRow :: A, 1, NSelector :: $A)
Subsequent rows in Column A: =IF(ROW()<COUNT(Input :: $B)/NSelector :: A:$A+2, A2+NSelector :: $A, "")
Data Subset, Column B, Rows 3
throuth the last: =IFERROR(INDIRECT(ADDRESS(A+1, 2, ,,"Input")), "")
Stats, Column A, Row 2: =IFERROR(MODE(Data Subset :: B), "No Mode")
Stats, Column B, Row 2: =COUNTIF(Data Subset :: B, A)
Lots of ways to skin this cat.
Jerry