Averages and Range (Copy)

Cheat Sheet: Mean, Median, Mode, and Range (IGCSE Mathematics 0580 – CORE)
Topic: Averages and Range (For Lists and Frequency Tables – Ungrouped Data)

1. Mean (Average)

• Formula for list:

Mean=Sum of all data valuesNumber of data valuestext{Mean} = frac{text{Sum of all data values}}{text{Number of data values}}

• Formula for frequency table:

Mean=Sum of (value × frequency)Total frequencytext{Mean} = frac{text{Sum of (value × frequency)}}{text{Total frequency}}

Purpose:

• Best for balanced, evenly spread data.
• Sensitive to extreme values (outliers).

2. Median (Middle Value)

• Arrange data in order.
• If odd number of data values:
  • Median = middle number.
• If even number of data values:
  • Median = mean of two middle numbers.

Purpose:

• Best for data with outliers or skewed distributions.
• Resistant to extreme values.

3. Mode (Most Frequent Value)

• Mode = data value that appears most often.
• If no value repeats → No mode.
• If two values repeat equally → Bimodal.

Purpose:

• Useful for finding the most common category or value.

4. Range (Spread of Data)

• Formula:

Range=Largest value−Smallest valuetext{Range} = text{Largest value} – text{Smallest value}

Purpose:

• Measures how spread out the data is.
• Sensitive to extreme values.

5. Quick Reference Table

6. Important Tips

• Always order data first when finding median.
• For frequency tables:
  • Multiply each value by its frequency to find the total sum for mean.
• Always state clearly which average you are using when answering questions.
• If comparing data, mention both mean/median (central tendency) and range (spread).

This cheat sheet fully covers all CORE-level knowledge for calculating and interpreting mean, median, mode, and range from lists and ungrouped frequency tables.