Home / iGCSE Mathematics (0580) :C9.3 Construct and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal intervals and scatter diagrams. iGCSE Style Questions Paper 3

iGCSE Mathematics (0580) :C9.3 Construct and interpret bar charts, pie charts, pictograms, stem-and-leaf diagrams, simple frequency distributions, histograms with equal intervals and scatter diagrams. iGCSE Style Questions Paper 3

IGCSE Mathematics(0580) Practice Questions Paper 3 - All Chapters
Question

(a) Students solve a puzzle by making guesses.
The table shows the number of guesses that each of 40 students make.

Number of guesses 1 2 3 4 5 6
Frequency 2 4 8 7 12 7

(i) Find the mode.
(ii) Calculate the mean.

(b) In another puzzle each student gets a score. These are the scores for 12 students:

17   21   24   32   27   11

26   18   10   29   14   24

(i) Complete the stem-and-leaf diagram for these scores.

(ii) Find the median.

(c) A different puzzle has three outcomes: win, draw or lose. The table shows the outcomes for 30 students:

Outcome Win Draw Lose
Frequency 9 14 7

Complete the pie chart to show this information.

▶️ Answer/Explanation
Solution

(a)(i) Ans: 5

The mode is the number with highest frequency, which is 5 (frequency 12).

(a)(ii) Ans: 4.1

Mean = (1×2 + 2×4 + 3×8 + 4×7 + 5×12 + 6×7) ÷ 40 = 164 ÷ 40 = 4.1

(b)(i) Ans:

1 | 0 1 4 7 8
2 | 1 4 4 6 7 9
3 | 2
Key: 1 | 7 represents 17

(b)(ii) Ans: 22.5

Ordered scores: 10,11,14,17,18,21,24,24,26,27,29,32. Median = average of 6th and 7th values = (21+24)/2 = 22.5

(c) Ans:

Pie chart angles: Win = (9/30)×360° = 108°, Draw = (14/30)×360° = 168°, Lose = (7/30)×360° = 84°

Question

(a) Zena records the number of letters she posts on each of 12 days.

3    7     3    8    7    1    0    6    5    1    7    2

(i) Write down the mode.
(ii) Find the median.

(b) Zena posts 6 parcels.

  • The lightest parcel has a mass of 4.6 kg.
  • The heaviest parcel has a mass of 6.2 kg.
  • The other 4 parcels have a mean mass of 5.01 kg.

Calculate the mean mass of the 6 parcels.

(c) Zena pays 105 euros to post a parcel.
The exchange rate is $1 = 0.84 euros.

Work out the cost in dollars to post the parcel.

(d) The cost to post a box increases from $22.68 to $44.

Work out the percentage increase in the cost.

(e) The diagram shows a parcel in the shape of a cuboid.

(i) Complete the net of the parcel on the 1 cm² grid.
Two faces have been drawn for you.

(ii) Find the volume of the parcel.

▶️ Answer/Explanation
Solution

(a)(i) Ans: 7

The mode is the most frequent number in the list. The number 7 appears three times, more than any other number.

(a)(ii) Ans: 4

First arrange the numbers in order: 0,1,1,2,3,3,5,6,7,7,7,8. The median is the average of the 6th and 7th numbers (3 and 5), which is 4.

(b) Ans: 5.14 kg

Total mass of 4 parcels = 4 × 5.01 = 20.04 kg. Total for all 6 parcels = 20.04 + 4.6 + 6.2 = 30.84 kg. Mean = 30.84 ÷ 6 = 5.14 kg.

(c) Ans: $125

Divide euros by exchange rate: 105 ÷ 0.84 = 125 dollars.

(d) Ans: 94%

Increase = $44 – $22.68 = $21.32. Percentage increase = (21.32 ÷ 22.68) × 100 ≈ 94%.

(e)(i) Ans: The net should show all six faces of the cuboid arranged flat, with dimensions 3cm×6cm, 3cm×2cm, and 6cm×2cm.

(e)(ii) Ans: 36 cm³

Volume = length × width × height = 3 × 6 × 2 = 36 cm³.

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