Mathematics • Year 7 • Unit 4 • Lesson 3
Frequency Tables — Real World
Apply tallies, frequency tables, class intervals and relative frequency to real settings: a canteen, a cricket scorecard, a class height survey, a goalkeeper's saves, and a music streaming summary.
1. Word problems
Build the table, then answer the questions. Show working — a single number with no working only earns half marks.
1.1 — Canteen lunch tally. Over one lunch break the canteen sold: 12 sandwiches, 8 pasta, 6 sushi, 9 wraps and 5 pies.
(a) Build a frequency table including a "Total" row.
(b) Calculate the relative frequency (3 d.p.) of "pasta" and convert it to a percentage. 3 marks
1.2 — Cricket scorecard. A batter's runs in 15 innings: 0, 12, 24, 8, 45, 3, 56, 22, 18, 9, 33, 0, 67, 14, 26.
(a) Group into class intervals 0–9, 10–19, 20–29, 30–39, 40–49, 50–59, 60–69.
(b) In which interval did the most innings fall?
(c) What fraction of innings produced 30 or more runs? 4 marks
1.3 — Class height survey. 24 Year 7 students' heights (cm): 142, 156, 148, 162, 151, 158, 145, 167, 153, 160, 149, 155, 171, 144, 159, 152, 165, 147, 154, 168, 150, 161, 146, 157.
(a) Group into class intervals of width 5 cm starting at 140 (140–144, 145–149, …).
(b) Which interval contains the most students?
(c) What is the relative frequency (3 d.p.) of students 160 cm or taller? 4 marks
1.4 — Goalkeeper's saves. In 12 matches a goalkeeper made these numbers of saves: 4, 6, 5, 3, 7, 6, 5, 8, 4, 6, 5, 7.
(a) Build a frequency table for every value from 3 to 8.
(b) Calculate cumulative frequency after each value. What does the final cumulative frequency equal? 3 marks
1.5 — Music streaming summary. A streaming app reports the number of minutes Maya listened to each genre last week: pop 240, rock 180, hip-hop 90, jazz 30, classical 60.
(a) Build a frequency table.
(b) Calculate relative frequency (3 d.p.) for each genre, and confirm they add to 1.000. 3 marks
2. Explain your thinking
Communication matters. Use full sentences. 4 marks
2.1 A classmate builds a frequency table for 30 test scores using class intervals 0–10, 10–20, 20–30, … and is confused because a score of exactly 20 could go in TWO intervals. In your own words, explain (i) why their intervals are problematic, (ii) two CORRECT ways to set up class intervals so each value belongs to exactly one interval, and (iii) why the total of all frequencies in a frequency table must always equal the number of data values.
How did this worksheet feel?
What I'll revisit before next class:
1.1 — Canteen lunch
(a) Sandwich 12, Pasta 8, Sushi 6, Wrap 9, Pie 5. Total = 12 + 8 + 6 + 9 + 5 = 40.
(b) Pasta relative frequency = 8 ÷ 40 = 0.200 = 20.0%.
1.2 — Cricket scorecard
(a) 0–9: 4 (0, 8, 3, 9); 10–19: 3 (12, 18, 14); 20–29: 3 (24, 22, 26); 30–39: 1 (33); 40–49: 1 (45); 50–59: 1 (56); 60–69: 2 (67 — wait, we have 67 only, plus... rechecking: 67 is 60–69, that's 1. Also need to check 22 which is 20–29. Final: 60–69: 1 (67)). Total = 4 + 3 + 3 + 1 + 1 + 1 + 1 = 14? Recheck: 0, 12, 24, 8, 45, 3, 56, 22, 18, 9, 33, 0, 67, 14, 26 = 15 innings. 0–9: 0, 8, 3, 0, 9 = 5; 10–19: 12, 18, 14 = 3; 20–29: 24, 22, 26 = 3; 30–39: 33 = 1; 40–49: 45 = 1; 50–59: 56 = 1; 60–69: 67 = 1. Total = 5 + 3 + 3 + 1 + 1 + 1 + 1 = 15 ✓.
(b) Most innings: 0–9 interval (5 innings).
(c) Innings of 30 or more: 1 + 1 + 1 + 1 = 4. Fraction = 4/15 ≈ 0.267 (26.7%).
1.3 — Class heights
(a) 140–144: 3 (142, 144, [also] — let me re-sort: 140–144 includes 142, 144 → 2). Sort approach: list and bin all 24 values. 142, 156, 148, 162, 151, 158, 145, 167, 153, 160, 149, 155, 171, 144, 159, 152, 165, 147, 154, 168, 150, 161, 146, 157.
140–144: 142, 144 → 2.
145–149: 148, 145, 149, 147, 146 → 5.
150–154: 151, 153, 152, 154, 150 → 5.
155–159: 156, 158, 155, 159, 157 → 5.
160–164: 162, 160, 161 → 3.
165–169: 167, 165, 168 → 3.
170–174: 171 → 1.
Total = 2 + 5 + 5 + 5 + 3 + 3 + 1 = 24 ✓.
(b) Three intervals tie with 5 students: 145–149, 150–154 and 155–159. (Accept any of these as the modal interval, or all three.)
(c) 160 cm or taller: 3 + 3 + 1 = 7. Relative frequency = 7 ÷ 24 ≈ 0.292 (29.2%).
1.4 — Goalkeeper saves
(a) 3: 1, 4: 2, 5: 3, 6: 3, 7: 2, 8: 1. Total = 1 + 2 + 3 + 3 + 2 + 1 = 12 ✓.
(b) Cumulative: after 3 → 1; after 4 → 3; after 5 → 6; after 6 → 9; after 7 → 11; after 8 → 12. The final cumulative frequency equals the total number of matches (12), because every match has been counted exactly once.
1.5 — Music streaming
(a) Pop 240, Rock 180, Hip-hop 90, Jazz 30, Classical 60. Total = 600 minutes.
(b) Pop: 240/600 = 0.400. Rock: 180/600 = 0.300. Hip-hop: 90/600 = 0.150. Jazz: 30/600 = 0.050. Classical: 60/600 = 0.100. Check: 0.400 + 0.300 + 0.150 + 0.050 + 0.100 = 1.000 ✓.
2.1 — Explain your thinking (sample response)
The classmate's intervals 0–10, 10–20, 20–30, … are problematic because the score 20 sits at the boundary between TWO intervals — should it go in 10–20 or in 20–30? Without a clear rule, two people might tally it differently and end up with totals that don't match. There are two correct ways to fix this. The first is to use integer-only intervals like 0–9, 10–19, 20–29, …, so each whole-number score belongs to exactly one row. The second is to use a "less than" rule, written as 0 ≤ x < 10, 10 ≤ x < 20, 20 ≤ x < 30, …, so a score of exactly 20 is put in the 20–<30 interval. Either way, every value goes in exactly one bin. The total of all frequencies must equal the number of data values because tallying counts each value once — if the frequencies don't add up to the data count, somewhere a value was missed or counted twice.
Marking: 1 for identifying the boundary problem; 1 for first correct fix (integer intervals); 1 for second correct fix (≤ x < rule); 1 for explaining why frequencies must sum to n.