Mean as Fair Share Examples in Statistics

Start with the recap, study the fully worked examples, then use the practice problems to check your understanding of Mean as Fair Share.

This page combines explanation, solved examples, and follow-up practice so you can move from recognition to confident problem-solving in Statistics.

Concept Recap

The mean (average) represents what each person would get if the total were divided equally among everyone.

Imagine 3 friends have 2, 4, and 9 candies. If they pool all candies (15 total) and share equally, each gets 5. That's the mean! It's the 'fair share' - what everyone would have if things were perfectly even.

Read the full concept explanation →

How to Use These Examples

  • Read the first worked example with the solution open so the structure is clear.
  • Try the practice problems before revealing each solution.
  • Use the related concepts and background knowledge badges if you feel stuck.

What to Focus On

Core idea: The mean is the value everyone would have if the total were distributed perfectly equally — a mathematical balance point for the data.

Common stuck point: Students add all the values but divide by the wrong number. Always divide by the count of values, not the number of categories.

Worked Examples

Example 1

easy
Five friends have 3, 7, 5, 10, and 5 sweets respectively. If they share all the sweets equally, how many does each person get?

Solution

  1. 1
    Step 1: Find the total number of sweets by adding all values: 3 + 7 + 5 + 10 + 5 = 30
  2. 2
    Step 2: The mean is the 'fair share' — divide the total equally among all 5 friends.
  3. 3
    Step 3: Calculate: \frac{30}{5} = 6 sweets each.

Answer

6 sweets each.
The mean as a fair share redistributes a total equally. This is the intuitive foundation of the arithmetic mean: total divided by count.

Example 2

medium
A student scores 72, 85, 90, and 69 on four tests. What score does she need on a fifth test to have a mean of 80?

Practice Problems

Try these problems on your own first, then open the solution to compare your method.

Example 1

easy
Four boxes contain 12, 8, 14, and 6 apples. Find the mean number of apples per box.

Example 2

easy
Three jars hold 9, 12, and 6 marbles. How many marbles must move from the second jar to the third jar so that all three jars have the same number?
← Back to Mean as Fair Share Practice Mode

Related Concepts

Weighted Average

Background Knowledge

These ideas may be useful before you work through the harder examples.

additiondivisionequal sharing