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JJ.1 Find the mean

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What is the mean?

The mean is the average of a set of numbers. It is found by adding all the numbers together and then dividing by how many numbers there are in the set.

Example:
  • For the numbers 5, 7, and 9: (5 + 7 + 9) ÷ 3 = 21 ÷ 3 = 7
  • The mean of 5, 7, and 9 is 7
Note

The mean gives us a single number that represents the "center" of a data set. It helps us understand what a typical value might be.

How to calculate the mean

To find the mean, follow these steps: add all the numbers in the data set, then divide by how many numbers are in the set.

Steps:
  • Step 1: Add all the numbers together
  • Step 2: Count how many numbers are in the set
  • Step 3: Divide the sum by the count
Note

Remember to add all values first, then divide. The order of operations is important!

Understanding the mean in real situations

The mean helps us understand data in everyday situations, like finding average test scores, temperatures, or amounts.

Example:
  • Sarah's test scores: 85, 92, 78, 90
  • Sum: 85 + 92 + 78 + 90 = 345
  • Count: 4 tests
  • Mean: 345 ÷ 4 = 86.25
  • Sarah's mean test score is 86.25
Note

The mean doesn't have to be one of the numbers in your original data set. It can be a decimal, even if all your original numbers are whole numbers.

When the mean can be misleading

Sometimes the mean doesn't give the best picture of a data set, especially when there are very high or very low values.

Example:
  • House prices on a street: $100,000, $110,000, $120,000, $130,000, $500,000
  • Mean: ($100,000 + $110,000 + $120,000 + $130,000 + $500,000) ÷ 5 = $192,000
  • But most houses cost around $115,000
Note

When there are extreme values (very high or very low numbers), the mean might not represent the data well. In these cases, the median might be more helpful.