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0580/42 Oct/Nov 2023, Question 2: Averages from Frequency Tables

Cambridge IGCSE Mathematics 0580 · Paper 42 (Extended) · Calculator · 11 marks

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The question, in short

From a frequency table of 50 homework marks and a list of 11 test scores, find averages, spread and a stem-and-leaf display.

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

Part (ai) · 1 mark

Write down the range of the homework marks from the frequency table.

  1. 1Range = 20 − 15 = 5

Answer5

Part (aii) · 1 mark

Write down the mode of the homework marks.

  1. 1Highest frequency is 19, for mark 17: mode = 17

Answer17

Part (aiii) · 1 mark

Find the median homework mark.

  1. 1Median is between the 25th and 26th marks
  2. 2Cumulative frequencies: 1, 4, 23, 34, so both are 18
  3. 3Median = 18

Answer18

Part (aiv) · 3 marks

Calculate the mean homework mark.

  1. 1Σfx = 1×15 + 3×16 + 19×17 + 11×18 + 10×19 + 6×20
  2. 2= 15 + 48 + 323 + 198 + 190 + 120 = 894
  3. 3Mean = 894 ÷ 50 = 17.88

Answer17.88

Part (bi) · 2 marks

Complete the stem-and-leaf diagram for Ed's 11 test scores using the given key.

  1. 1In order: 18, 20, 20, 21, 21, 21, 22, 25, 30, 33, 34
  2. 21 | 8
  3. 32 | 0 0 1 1 1 2 5
  4. 43 | 0 3 4

Answer| 1 | 8 | | 2 | 0 0 1 1 1 2 5 | | 3 | 0 3 4 |

Part (bii) · 1 mark

Find the median of Ed's test scores.

  1. 111 scores, median is the 6th value = 21

Answer21

Part (biii) · 2 marks

Find the interquartile range of Ed's test scores.

  1. 1In order: 18, 20, 20, 21, 21, 21, 22, 25, 30, 33, 34
  2. 2Lower quartile = 3rd value = 20; upper quartile = 9th value = 30
  3. 3IQR = 30 − 20 = 10

Answer10

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