Let's start with some test data:
person_id <- c("1","2","3","4","5","6","7","8","9","10")
inches <- as.numeric(c("56","58","60","62","64","","68","70","72","74"))
height <- data.frame(person_id,inches)
height
person_id inches
1          1     56
2          2     58
3          3     60
4          4     62
5          5     64
6          6     NA 
7          7     68
8          8     70
9          9     72
10        10     74
The blank was already replaced with NA in height$inches. 
You could also do this yourself:
height$inches[height$inches==""] <- NA
Now to fill in the NA with the average from the non-missing values of inches. 
options(digits=4)
height$inches[is.na(height$inches)] <- mean(height$inches,na.rm=T)
height
   person_id inches
1          1  56.00
2          2  58.00
3          3  60.00
4          4  62.00
5          5  64.00
6          6  64.89
7          7  68.00
8          8  70.00
9          9  72.00
10        10  74.00