When you're in Year 10 math, it's important to understand some basic ways to measure data. These methods help us sum up a bunch of numbers with one main value. The three main methods are mean, median, and mode. Let’s break them down in a simple way!

1. Mean

The mean is often just called the average. To find the mean, you add all the numbers together and then divide by how many numbers there are.

How to Calculate Mean:

• Add up all the values.
• Divide that total by the number of values.

Example:
Let’s say we have these numbers: 5, 8, 12, 15.

• First, add the numbers: $5 + 8 + 12 + 15 = 40$.
• Now, divide by how many numbers there are, which is 4:
  $\text{Mean} = \frac{40}{4} = 10.$

So, the mean of these numbers is 10.

2. Median

The median is the number that is right in the middle when you line up your data from smallest to largest. If there’s an odd number of numbers, the median is just the middle one. If there’s an even number, you find the average of the two middle numbers.

Example:
Using the numbers 5, 8, 12, 15:

• They are already in order.
• Since there are 4 numbers (even), find the median like this:
  $\text{Median} = \frac{8 + 12}{2} = \frac{20}{2} = 10.$

If we had another set of numbers: 5, 8, 12, 15, 20 (five numbers):

• The middle number is 12, so that’s the median.

3. Mode

The mode is the number that shows up the most in your data set. Sometimes, a set can have one mode, more than one mode (which we call bimodal or multimodal), or no mode at all if all numbers are different.

Example:
Look at this set: 5, 8, 8, 12, 15.

• Here, the number 8 shows up the most (twice), so the mode is 8.

In another case, with the numbers 5, 8, 12, 15, each number is different and appears only once, so there is no mode.

Summary

• Mean: This is the average. You find it by adding all the numbers and dividing by how many there are.
• Median: This is the middle value when the numbers are lined up in order.
• Mode: This is the number that appears the most in the data.

Knowing these differences is really helpful. They can give you different views of your data. For example, if your data is skewed, the mean can be affected a lot by very high or low numbers, while the median can give a better idea of what's typical. Remember these definitions and examples as you learn more about data handling!