Quick questions on Frequency and grouped frequency tables for HSC Maths Standard 2

When the data takes only a few distinct values - shoe sizes, goals per game, number of pets - you do not need to group anything. List each distinct value in its own row from smallest to largest, tally the raw data into those rows, and write the frequency beside each. The tally column is not decoration: tallying in one careful pass is what stops you losing or repeating a value, and the gate-of-five grouping makes the strokes quick to count.

When the data is spread over a wide range - test marks out of $100$, masses in grams, commute times - a row for every distinct value would be unreadable. Instead you group the data into class intervals (also called classes), each covering an equal-width band of values, and count how many data values fall in each band.

Once data is grouped you no longer know each exact value, only the class it sits in. The class centre is the value used to stand in for everything in that class: it is the midpoint of the interval, found by averaging the lower and upper limit.

The cumulative frequency of a row is the total of that row's frequency and all the frequencies above it - a running total down the table. It answers "how many data values are at most this size". You build it by carrying a running sum: start with the first frequency, then add each next frequency to the total so far.