Mathematics • Year 7 • Unit 4 • Lesson 3
Frequency Tables
Build fluency with tallying, building a frequency table, grouping into class intervals, and calculating relative frequency. Tallies turn raw data into a clear picture in seconds — and the total of all frequencies always equals the number of data values.
1. I do — fully worked example
Read every line. Each step has a short reason on the right so you can see why, not just what.
Problem. A teacher records the number of pets owned by 15 students: 2, 0, 1, 3, 2, 1, 0, 2, 1, 2, 3, 1, 0, 2, 1. Build a complete frequency table with tallies, frequency and relative frequency.
Step 1 — List the possible values.
Possible counts: 0, 1, 2, 3 (every value from the smallest to the largest).
Reason: a frequency table needs one row for every value that could appear.
Step 2 — Tally each data value once.
0 → ||| (3) 1 → |||| (5) 2 → |||| (5) 3 → || (2)
Reason: cross every fifth tally (||||) to form a gate of 5 — makes counting fast.
Step 3 — Add up. Total = 15. Matches our data set.
3 + 5 + 5 + 2 = 15 ✓
Reason: if the frequencies don't add to the number of values, you've tallied wrong.
Step 4 — Relative frequency = frequency ÷ total.
0: 3/15 = 0.200 (20%) 1: 5/15 ≈ 0.333 (33.3%)
2: 5/15 ≈ 0.333 (33.3%) 3: 2/15 ≈ 0.133 (13.3%)
Reason: relative frequency turns counts into proportions — useful for comparison.
Answer (frequency table):
Pets Tally Freq Rel. freq
0 ||| 3 0.200
1 |||| 5 0.333
2 |||| 5 0.333
3 || 2 0.133
Total 15 1.000
2. We do — fill in the missing entries
20 students were asked their shoe size. Build the frequency table. 4 marks
Data: 7, 8, 7, 9, 8, 7, 8, 10, 9, 7, 8, 8, 9, 7, 10, 8, 9, 7, 8, 9.
Step 1 — list possible values: 7, 8, 9, 10.
Step 2 — tally each value once, then count.
Size 7: Tally _______________ Freq _____
Size 8: Tally _______________ Freq _____
Size 9: Tally _______________ Freq _____
Size 10: Tally _______________ Freq _____
Step 3 — check the total.
Frequencies should add to _____ (number of students).
Step 4 — relative frequency (3 d.p.) for size 8.
Size 8 relative frequency = ____ / 20 = _______
3. You do — independent practice
Show your tally and frequencies clearly. Cross-check the totals before moving on.
Foundation — simple tally
3.1 10 students rolled a 6-sided die. Results: 3, 5, 2, 6, 3, 1, 4, 3, 5, 6. Build a frequency table for the values 1–6. 1 mark
3.2 A class of 20 named their favourite ice-cream: chocolate (6), vanilla (4), strawberry (5), mint (3), mango (2). Build a frequency table and check the total. 1 mark
3.3 A class of 25 reported how many siblings they have: data 0, 1, 2, 1, 0, 2, 1, 3, 1, 0, 2, 1, 1, 0, 4, 2, 1, 1, 0, 1, 2, 0, 1, 1, 2. Build a frequency table. 1 mark
3.4 From the table in 3.3, calculate the relative frequency (decimal, 3 d.p.) of students with exactly 1 sibling. 1 mark
Standard — group into intervals
3.5 12 students sat a maths test. Scores out of 100: 34, 56, 72, 45, 61, 38, 55, 79, 43, 68, 52, 77. Group into class intervals of width 10 (30–39, 40–49, …, 70–79) and give the frequency for each interval. 2 marks
3.6 A class of 30 reported their favourite subject: Maths 12, English 8, Science 10. Calculate the relative frequency (3 d.p.) AND percentage (1 d.p.) for each subject. 2 marks
Extension — push your thinking
3.7 A frequency table for 40 daily commutes has these frequencies: 0–9 min: 7, 10–19 min: 15, 20–29 min: 11, 30–39 min: 5, 40–49 min: ?. Find the missing frequency and the relative frequency (3 d.p.) of the 30–39 min interval. 3 marks
3.8 Cumulative frequency is a running total of frequencies. Use the 12-student test data from 3.5 to write the cumulative frequency after each class interval. What does the final cumulative frequency equal, and why? 2 marks
How did this worksheet feel?
What I'll revisit before next class:
Section 2 — Shoe sizes (We do)
Size 7: 6 students. Size 8: 7 students. Size 9: 5 students. Size 10: 2 students.
Check: 6 + 7 + 5 + 2 = 20 ✓.
Relative frequency of size 8: 7 ÷ 20 = 0.350.
3.1 — Die rolls
1: 1, 2: 1, 3: 3, 4: 1, 5: 2, 6: 2. Total = 10 ✓.
3.2 — Ice-cream
chocolate 6, vanilla 4, strawberry 5, mint 3, mango 2. Total = 6 + 4 + 5 + 3 + 2 = 20 ✓.
3.3 — Siblings (n = 25)
0: 6, 1: 11, 2: 6, 3: 1, 4: 1. Total = 6 + 11 + 6 + 1 + 1 = 25 ✓.
3.4 — Relative frequency of "1 sibling"
11 ÷ 25 = 0.440 (or 44.0%).
3.5 — Test scores grouped (n = 12)
30–39: 2 (scores 34, 38).
40–49: 2 (scores 45, 43).
50–59: 3 (scores 56, 55, 52).
60–69: 2 (scores 61, 68).
70–79: 3 (scores 72, 79, 77).
Total = 2 + 2 + 3 + 2 + 3 = 12 ✓.
3.6 — Favourite subjects
Maths: 12 ÷ 30 = 0.400 (40.0%).
English: 8 ÷ 30 ≈ 0.267 (26.7%).
Science: 10 ÷ 30 ≈ 0.333 (33.3%).
Check: 40.0% + 26.7% + 33.3% = 100% ✓.
3.7 — Missing commute frequency
Total of given frequencies: 7 + 15 + 11 + 5 = 38. Missing frequency = 40 − 38 = 2.
Relative frequency of 30–39 min interval: 5 ÷ 40 = 0.125 (12.5%).
3.8 — Cumulative frequency for test scores
After 30–39: 2. After 40–49: 2 + 2 = 4. After 50–59: 4 + 3 = 7. After 60–69: 7 + 2 = 9. After 70–79: 9 + 3 = 12.
The final cumulative frequency equals 12 — the same as the total number of data values, because every value has been counted exactly once across the intervals.