How do you calculate the mean and range of a set of numbers?

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Calculating the mean and range of a set of numbers is a fundamental aspect of descriptive statistics, which helps in understanding the data better. Let’s break down each computation step-by-step.

Calculating the Mean

The mean, often referred to as the average, is found by adding all the numbers in a dataset and then dividing that sum by the number of values in the dataset. Here’s how you can do it:

  1. Step 1: Sum all the numbers in your dataset. For example, if you have the numbers 4, 8, 6, 5, and 3, you first add them together:
    • 4 + 8 + 6 + 5 + 3 = 26
  2. Step 2: Count the total number of values. In our case, we have 5 numbers.
  3. Step 3: Divide the sum by the count of numbers:
    • Mean = Sum of the numbers / Count = 26 / 5 = 5.2

So, the mean of the dataset {4, 8, 6, 5, 3} is 5.2.

Calculating the Range

The range gives you an idea of how spread out the values in your dataset are. To find the range, you simply subtract the smallest number from the largest number:

  1. Step 1: Identify the largest number in your dataset. For our example, the numbers are 4, 8, 6, 5, and 3; thus, the largest number is 8.
  2. Step 2: Identify the smallest number, which in this case is 3.
  3. Step 3: Subtract the smallest number from the largest number:
    • Range = Largest number – Smallest number = 8 – 3 = 5

This means the range of the dataset {4, 8, 6, 5, 3} is 5.

Conclusion

In summary, the mean provides a central value of the dataset, while the range offers insight into the variability of the data. Together, they serve as essential tools for statistical analysis, aiding in making sense of numbers in a meaningful way.

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