Measures of Centre (Junior Cert Mathematics): Revision Notes

Measures of Centre

In this section, you'll learn about three important ways to find the "middle" or "average" of a set of numbers. These are called mean, median, and mode. Each of them gives you a different way to understand the data, and they are very useful in maths.

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1. Mean (Average)

What it is:

The mean is what most people think of as the "average." It tells you the total amount shared equally among all the numbers. For example, if you and your friends each have different amounts of pocket money, the mean would tell you how much each of you would have if you shared the money equally.

How to calculate it:

• Step 1: Add up all the numbers.
• Step 2: Divide the total by how many numbers there are. Formula:

$\text{Mean} = \frac{\text{Total of all numbers}}{\text{Number of numbers}}$

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2. Median

What it is:

The median is the middle number in a list of numbers when they are arranged from smallest to largest. If there are two middle numbers (because there's an even number of numbers), the median is the average of those two middle numbers.

How to calculate it:

• Step 1: Arrange the numbers from smallest to largest.
• Step 2: Find the middle number. If there are two middle numbers, find their average.

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3. Mode

What it is:

The mode is the number that appears most often in a list of numbers. There can be more than one mode if two or more numbers appear the most often. If no number repeats, then there is no mode.

How to calculate it:

• Step 1: Look for the number that shows up the most.

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Advantages and Disadvantages of Mean, Median, and Mode

Mean:

• Advantages: Uses all the data, giving a true average. Good for further calculations.
• Disadvantages: Easily affected by outliers (extremely high or low values).

Median:

• Advantages: Not affected by outliers. Represents the middle value in the data.
• Disadvantages: Doesn't consider all data points, only the order.

Mode:

• Advantages: Shows the most common value. Works with both numbers and categories.
• Disadvantages: Might not exist if no number repeats, and can ignore much of the data.

Choosing the Right Measure

• Use the mean for a true average when data is balanced.
• Use the median to avoid outliers and find the middle value.
• Use the mode to identify the most common value in your data.

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Key Points to Remember

• Mean: Add up all the numbers and divide by how many there are. This gives you the "average."
• Median: Put the numbers in order and find the middle one. If there are two middle numbers, take their average.
• Mode: Find the number that appears most often. There can be more than one mode, or none at all. By learning how to calculate the mean, median, and mode, you'll be able to summarise data in different ways. These skills are important not only in maths but also in understanding everyday information, like figuring out average scores, finding the most common result, or identifying the middle value in a set of numbers.

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