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0580/32 May/Jun 2024, Question 4: Tally Charts and Frequency Tables

Cambridge IGCSE Mathematics 0580 · Paper 32 (Core) · Calculator · 14 marks

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The question, in short

Anton surveys 50 families on pet numbers; use the table and the rule about 4-pet and 5-pet families to complete the table, bar chart, mode and mean, then handle 80 cats, rabbits and hamsters in a pie chart and probability.

Summarised in our own words. Use the official paper for the exact wording and the diagram.

Part (ai) · 3 marks

Using 50 families total and twice as many with 4 pets as with 5, find the missing frequencies for 4 and 5 pets.

  1. 1Families with 4 or 5 pets = 50 − (5 + 12 + 15 + 9) = 9
  2. 24 pets : 5 pets = 2 : 1, so 5 pets = 9 ÷ 3 = 3
  3. 34 pets = 2 × 3 = 6

Answer| Number of pets | 4 | 5 | | Number of families | 6 | 3 |

Part (aii) · 2 marks

Draw the missing bars on the bar chart for numbers of pets 1 to 5 using your completed frequencies.

  1. 1Families shown so far: 5 + 12 + 15 + 9 = 41
  2. 2So 4 pets and 5 pets share 50 − 41 = 9 families.
  3. 3Twice as many have 4 pets: 4 pets = 6, 5 pets = 3.
  4. 4Draw bars of heights 12, 15, 9, 6 and 3 for 1 to 5 pets: correct bar chart.

AnswerCorrect bar chart

Part (aiii) · 1 mark

State the number of pets that occurs most often among the families.

  1. 1Highest frequency is 15 for 2 pets: mode = 2

Answer2

Part (aiv) · 3 marks

Calculate the mean number of pets per family using all 50 families and the completed frequencies.

  1. 14 and 5 pets: 50 − 41 = 9 families, split 6 and 3.
  2. 2Total pets = 0×5 + 1×12 + 2×15 + 3×9 + 4×6 + 5×3 = 108
  3. 3Mean = 108 ÷ 50 = 2.16

Answer2.16

Part (bi) · 2 marks

For 38 cats, 28 rabbits and 14 hamsters out of 80, work out each sector angle and complete the table.

  1. 1360 ÷ 80 = 4.5° per pet
  2. 2Cat 38 × 4.5 = 171°, Rabbit 28 × 4.5 = 126°, Hamster 14 × 4.5 = 63°

Answer| Type of pet | Pie chart sector angle | | Cat | 171 | | Rabbit | 126 | | Hamster | 63 |

Part (bii) · 2 marks

Draw the pie chart sectors for cats, rabbits and hamsters using the angles found, starting from the given radius.

  1. 1From the vertical radius, measure 171° for Cat, then 126° for Rabbit
  2. 2The remaining 63° is Hamster; label each sector

AnswerCorrect pie chart drawn

Part (biii) · 1 mark

Find the probability that a randomly chosen pet is a rabbit, using 28 rabbits out of 80 pets.

  1. 1P(rabbit) = 28/80 = 7/20

Answer7/20

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Also searched as: 0580/32/M/J/24 · 0580_s24_qp_32 · 0580 s24 32 · question 4.
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