A frequency table lists each value and how many times it occurred. The skill is keeping two columns apart in your head: the value, and the count of that value.
What is the small gap?
Both columns hold numbers, so they get mixed. A student asked “how many students were surveyed?” adds the values (shoe sizes) instead of the frequencies. The question asks for a count, and counts live in the frequency column.
How do you read a table step by step?
- Read the column headings and say what each one means in words.
- Read one row aloud: “3 students have a shoe size of 6”.
- Add the frequency column for the total number of items.
- Only then answer the question.
A scaffolded example
An original table: the number of books 30 Form 4 students borrowed in a month.
| Books borrowed | Frequency |
|---|---|
| 0 | 6 |
| 1 | 9 |
| 2 | 8 |
| 3 | 5 |
| 4 | 2 |
The total is 6 + 9 + 8 + 5 + 2 = 30, which matches the class size.
How many borrowed at least 3 books? Rows 3 and 4: 5 + 2 = 7 students. What fraction is that? 7/30.
The total number of books borrowed needs each row multiplied: 0×6 + 1×9 + 2×8 + 3×5 + 4×2 = 0 + 9 + 16 + 15 + 8 = 48.
What does the common mistake look like?
A student adds the values 0 + 1 + 2 + 3 + 4 = 10 and writes “10 students”. The class has 30. The check in step 3 prevents this: the frequency column must sum to the stated number of items.
Self-check
Using the table above, how many students borrowed fewer than 2 books? What percentage is that?
Answer
Fewer than 2 means 0 or 1 book: 6 + 9 = 15 students.
The percentage is 15/30 × 100 = 50%.
Note that “fewer than 2” does not include the 2-book row.
Where does this show up in SPM?
In SPM Mathematics, frequency tables lead to mean, histograms and ogives. In Science, results tables have the same shape, and a careful reading habit carries over to reading a graph before concluding.
Go on to calculating mean, median and mode, or back to the probability and data basics hub.
One-to-one Mathematics tuition starts with a one-hour trial class (from RM50).