📊 Statistics and Data

KS3 Mathematics Worksheet

🎓 Mini-Lesson: Averages and Range

What are Averages?

Averages are ways to find a "typical" or "middle" value in a set of data. We use three different types of averages: mean, median, and mode.

Mean (Average)

The mean is the total of all values divided by how many values there are.

Mean = Sum of all values ÷ Number of values
Example: Find the mean of 3, 7, 5, 9, 6
  1. Add all values: 3 + 7 + 5 + 9 + 6 = 30
  2. Count how many values: 5 values
  3. Divide: 30 ÷ 5 = 6
  4. Mean = 6
Median (Middle Value)

The median is the middle value when the data is arranged in order.

Steps:
1. Put the values in order from smallest to largest
2. Find the middle value
Example: Find the median of 7, 3, 9, 5, 6
  1. Put in order: 3, 5, 6, 7, 9
  2. Find the middle: 6 (third value out of five)
  3. Median = 6
Example with even number of values: 4, 7, 2, 9
  1. Put in order: 2, 4, 7, 9
  2. Two middle values: 4 and 7
  3. Find the mean of the two: (4 + 7) ÷ 2 = 5.5
  4. Median = 5.5
Mode (Most Common)

The mode is the value that appears most often.

Example: Find the mode of 3, 7, 5, 7, 9, 7, 2
  1. Count how many times each value appears:
    2 appears 1 time, 3 appears 1 time, 5 appears 1 time,
    7 appears 3 times, 9 appears 1 time
  2. Mode = 7 (appears most often)
Special Cases:
  • If no value repeats, there is no mode
  • If two values appear equally most often, there are two modes (bimodal)
Range (Spread of Data)

The range shows how spread out the data is.

Range = Highest value - Lowest value
Example: Find the range of 3, 7, 12, 5, 9
  1. Find highest value: 12
  2. Find lowest value: 3
  3. Subtract: 12 - 3 = 9
  4. Range = 9
Quick Comparison:
Measure What it tells us When to use
Mean The average of all values When you want to know the typical value
Median The middle value When there are extreme values (outliers)
Mode The most common value When you want to know what's most popular
Range How spread out the data is When you want to know the variability

💡 Remember: Always show your working! It helps you check your answer and get marks even if you make a small mistake.

✏️ Practice Questions

Calculate the mean, median, mode, or range as requested.