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JJ.3 Find the median

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What is the median?

Median is the middle number in a set of numbers that is arranged in order from least to greatest. It shows the value that lies in the center of the data set.

Example:
  • Data set: 3, 7, 9 → Median is 7 (the middle number)
  • Data set: 2, 5, 6, 8, 10 → Median is 6
Note

Always make sure the numbers are in order before finding the median.

How to find the median

To find the median, organize the numbers from least to greatest and find the number in the middle. If there is no single middle number, find the average of the two middle numbers.

Steps:
  • Arrange the numbers: 4, 1, 3, 9 → 1, 3, 4, 9
  • Since there are 4 numbers, take the two middle numbers: 3 and 4
  • Find the average: (3 + 4) ÷ 2 = 3.5 → Median is 3.5
Note

When there are two middle numbers, the median might be a whole number or a decimal.

When is the median useful?

The median is helpful when you want to know the center of a data set, especially when very large or very small numbers might make the mean less accurate.

Example:
  • Test scores: 40, 75, 80, 85, 90, 100
  • Median is 82.5, which shows the middle score better than the mean when there is an outlier like 40 or 100.
Note

The median helps show the "typical" number in a group, even when one number is much higher or lower than the rest.

Using median in real life

The median is used in real life to find middle values, such as typical house prices, average incomes, or test results.

Example:
  • If house prices are $150,000, $200,000, $275,000, $1,000,000, the median gives a better idea of a typical price than the mean.
Note

Median helps avoid being influenced by extremely high or low numbers when making decisions.

Check your understanding

When finding the median, always ask yourself: Did I put the numbers in order? Do I have one middle number or two?

Try it:
  • Data set: 5, 12, 8, 3, 10.
  • Step 1: Arrange → 3, 5, 8, 10, 12
  • Step 2: Median is 8
Note

If you can explain how you found the median, you understand the concept well.