Q.The average of 4 positive integers is 39. The highest integer is 73 and the lowest integer is 19. The difference between the remaining two integers in 18. Find the remaining integers.

What Does "Average" Really Mean?

Imagine you and three friends share a pizza. The pizza has 8 slices. If you divide it equally, each person gets 2 slices. That "2" is the average number of slices per person.

The core idea is simple: the average is a single number that represents a whole group of numbers — it's the "fair share" if everything were distributed equally.

The Intuition: Balancing the Scale

Think of a seesaw. If you put weights at different positions, the seesaw tilts. The average is the balancing point — the single position where the seesaw would stay level if all the weights were the same.

For example, consider the numbers 2, 4, and 6. Their average is 4. Notice how 2 is 2 below 4, and 6 is 2 above 4 — they balance perfectly around 4.

The Precise Definition

The most common average — called the arithmetic mean — is defined as:

That's it. Add everything up, then divide by how many things you added.

Example

Find the average of: 5, 8, 12, 15

1. Sum: $5 + 8 + 12 + 15 = 40$
2. Count: There are 4 numbers.
3. Divide: $40 \div 4 = 10$

The average is 10.

Why Does This Work?

The formula is just a compact way of saying: "If every value were the same, what would that common value be?"

Suppose you have test scores: 70, 80, 90. The sum is 240. If all three scores were equal, each would be $240 \div 3 = 80$. So 80 is the average — the number that, repeated three times, gives the same total.

A Common Misunderstanding

Many students think the average is "the most common value" or "the middle value." It's not.

• Average (mean): the balancing point — sensitive to every number.
• Median: the middle value when sorted.
• Mode: the most frequent value. …