Measures of Spread

Once you know the centre of your data (like the mean or median), it's also important to see how spread out the data is. This helps you understand if the numbers are close together or far apart. Two ways to measure the spread of data are the Range and the Interquartile Range (IQR). These will help you see how much the data varies.

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1. Range

What it is**:**

The range is the simplest way to measure how spread out the numbers in your data are. It shows the difference between the largest and smallest numbers in your data. Think of it as the distance between the highest and lowest points.

How to calculate it:

1. Find the highest number in your data.
2. Find the lowest number in your data.
3. Subtract the lowest number from the highest number. The answer is the range.

Why use it?

• Easy to calculate: The range is simple and quick to find.

• Good for a quick look: It gives you a general idea of how spread out the data is. What to watch out for:

• Sensitive to outliers: If there's a really high or low number that's very different from the rest, it can make the range bigger than it should be.

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2. Interquartile Range (IQR)

What it is:

The interquartile range (IQR) measures the spread of the middle half of your data. It ignores the highest and lowest parts of the data and focuses on the middle 50%. The IQR is found by subtracting the first quartile (Q1) from the third quartile (Q3). Q1 and Q3 are the medians of the lower half and upper half of the data, respectively.

How to calculate it:

4. Arrange the numbers in order from smallest to largest.
5. Find Q1 (the first quartile): This is the median of the lower half of the data.
6. Find Q3 (the third quartile): This is the median of the upper half of the data.
7. Subtract Q1 from Q3. The answer is the IQR.

Why use it?

• Good for data with outliers: The IQR isn't affected by extreme values, so it gives a better idea of the spread for most of the data.

• Focuses on the middle: It tells you how spread out the central part of your data is. What to watch out for:

• More steps to calculate: It takes a little more work than finding the range, but it gives you a better idea of the spread when there are outliers.

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Key Points to Remember

• Range: The difference between the highest and lowest values. It's easy to find but can be thrown off by very high or low numbers (outliers).
• Interquartile Range (IQR): The range of the middle 50% of the data. It's more reliable when you have outliers because it ignores the extremes.

These measures of spread help you see how much your data varies, giving you a clearer picture of the numbers as a whole. Understanding both the range and the IQR will help you describe your data more accurately.