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Mastering Averages Together

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Mastering Averages Together

Students working with data and calculations

📊 Part 1: Understanding Averages

Key Vocabulary:

Mean: Add all numbers and divide by how many numbers there are

Mode: The number that appears most often

Median: The middle number when data is ordered from smallest to largest

Range: The difference between the largest and smallest numbers

1. Match each term with its correct definition:

a) Mode _________ The middle value when data is ordered

b) Mean _________ The most frequently occurring value

c) Median _________ The difference between highest and lowest values

d) Range _________ The total divided by the number of values

2. For the data set: 3, 7, 5, 3, 8, 5, 3

What is the mode?

3

5

7

8

🔢 Part 2: Step-by-Step Calculations

3. Calculate all four averages for the data set: 4, 6, 2, 8, 5

Step 1 - Order the data: ___________________

Mode: _______ (Which number appears most often?)

Median: _______ (What is the middle number?)

Mean: Total = _____ ÷ _____ = _____

Range: _____ - _____ = _____

4. A football team scored these goals in 6 matches: 1, 3, 2, 3, 0, 3

Ordered data: ___________________

Mode: _____ goals

Median: _____ goals

Mean: _____ goals

Range: _____ goals

5. The temperatures (°C) recorded over a week were: 12, 15, 18, 15, 20, 16, 14

Calculate the mean temperature: ______________

What was the range of temperatures? ______________

💭 Part 3: Problem Solving

6. Sarah's test scores are: 78, 82, 85, 78, 92. She needs a mean score of 83 to get a merit certificate. Does she qualify?

Show your working:

Mean = ___________________

Does she qualify? _____ Explain: ___________________

7. A data set has 5 numbers. The mode is 7, the median is 8, and the range is 6. If the smallest number is 4, what could the data set be?
8. True or False? Tick all correct statements:

A data set can have more than one mode

The mean is always one of the numbers in the data set

The median is always the middle number when data is ordered

The range tells us how spread out the data is

9. Extension Challenge: The mean of 4, 7, x, 9 is 8. What is the value of x?

Working: Mean = 8, so total = 8 × 4 = _____

4 + 7 + x + 9 = _____

Therefore: x = _____

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