DISCRETE NUMERICAL VALUE : the data for which the values are discrete, certain, known.
for example: 1) rolling a die. now I know the values / outcomes that might appear. and hence the observation can only take certain values.
2) when the customers are asked to rate the quality of services provided, all the possible outcomes are already known to us. and hence the data set will only include specific and certain particular values.
3) lets assume that a teacher is asked to choose 8 children out of a class of 32 students at random. the teacher calls out 8 distinct roll nos. so in this case, all the possible outcomes in all 8 rounds of selection were known and discrete and certain to all students and audience.
CONTINUOUS NUMERICAL VALUE : the data for which the values are unknown.
for example: 1) the heights of all the students of grade 12 were recorded by a school. now here, we do not know the exact values of the heights that is to be calculated. the heights of two students can be 152cm and 176.65cm resp. now here we couldn't have guessed or known the values the heights_of the students would take.
ALSO , discrete numerical values are the values that can be counted. and continuous numerical values are values that can be measured.
hope this helps. please let me know if you have any other doubts.