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Worked Examples

Statistics

Working through solved examples is one of the most effective ways to master statistics & probability in IGCSE Mathematics. These worked examples, curated by Teacher Rig, cover the most common question

Working through solved examples is one of the most effective ways to master statistics & probability in IGCSE Mathematics. These worked examples, curated by Teacher Rig, cover the most common question types you will encounter in the Cambridge IGCSE 0580 exam. Each solution shows every step of working with clear explanations of the reasoning behind each step.

Example 1: Estimating the mean from a grouped frequency table

Foundation Similar to 0580/22/M/J/22 Q19

Question

The table shows the heights of 50 plants. Height (cm): 0-10 (freq 5), 10-20 (freq 12), 20-30 (freq 18), 30-40 (freq 10), 40-50 (freq 5). Estimate the mean height.

Solution

  1. 1

    Find the midpoint of each class

    Midpoints: 5, 15, 25, 35, 45

    Midpoint = (lower + upper) / 2 for each class.

  2. 2

    Calculate midpoint times frequency for each class

    5x5=25, 15x12=180, 25x18=450, 35x10=350, 45x5=225

    Each midpoint represents all values in that class.

  3. 3

    Sum the products and divide by total frequency

    Sum = 25+180+450+350+225 = 1230. Mean = 1230/50 = 24.6 cm

    Estimated mean = sum of (midpoint x frequency) / total frequency.

Final Answer: Estimated mean = 24.6 cm

Exam Tip

This is an ESTIMATE because we use midpoints as representative values. The question will say estimate, which tells you to use midpoints.

Example 2: Cumulative frequency and median

Extended Similar to 0580/42/M/J/23 Q5

Question

Draw a cumulative frequency curve and find the median and interquartile range. Masses (kg): 40-50 (freq 3), 50-60 (freq 7), 60-70 (freq 15), 70-80 (freq 12), 80-90 (freq 8), 90-100 (freq 5).

Solution

  1. 1

    Calculate cumulative frequencies

    50: 3, 60: 10, 70: 25, 80: 37, 90: 45, 100: 50

    Add each frequency to the running total. Plot at upper class boundaries.

  2. 2

    Find the median position

    Total = 50, so median is at 50/2 = 25th value

    The median is at the n/2 position on the cumulative frequency axis.

  3. 3

    Read the median from the curve

    At cumulative frequency 25, read across to the curve and down to get approximately 70 kg

    Draw a horizontal line from 25 on the y-axis to the curve, then draw vertically down to read the x-value.

  4. 4

    Find the quartiles and IQR

    LQ at 50/4 = 12.5th value, approximately 62 kg. UQ at 3(50)/4 = 37.5th value, approximately 80 kg. IQR = 80 - 62 = 18 kg.

    Lower quartile at n/4, upper quartile at 3n/4. IQR = UQ - LQ.

Final Answer: Median approximately 70 kg, IQR approximately 18 kg

Exam Tip

Plot cumulative frequency at the UPPER class boundary, not the midpoint. Join points with a smooth S-shaped curve.

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Frequently Asked Questions

How many statistics & probability questions appear in the IGCSE exam?

Statistics & Probability typically appears in both Paper 2 (non-calculator) and Paper 4 (calculator). You can expect 2-4 questions on statistics & probability across both papers, worth a combined 15-25 marks depending on the session.

What is the best way to practise statistics & probability for IGCSE?

Start by understanding the methods through worked examples like these, then practise past paper questions under timed conditions. Teacher Rig recommends working through at least 20 statistics & probability past paper questions before your exam, checking your method against mark schemes.

Should I memorise statistics & probability formulas for the exam?

Some formulas are given on the formula sheet in the exam, but you should still be very familiar with them. Key formulas that are NOT on the sheet should be memorised. Practice using the formulas so that applying them becomes automatic.

Need Help with Statistics?

Book a free 60-minute trial class with Teacher Rig. Work through Statistics problems together and build your confidence.