What are Mean, Median, Mode, and Range?

Mean, median, mode, and range are fundamental concepts in descriptive statistics. They provide a quick and simple summary of the key characteristics of a data set. Understanding what each one represents is crucial for data analysis.

Mean (The Average)

The mean is the most common measure of central tendency, often referred to as the "average."

• How to Calculate: Add up all the numbers in the data set and then divide by the total count of numbers.
• Example: For the set {2, 4, 6, 8}, the sum is 20. The count is 4. The mean is 20 / 4 = 5.
• When to Use: Use the mean when your data is not heavily skewed by outliers (extremely high or low values).

Median (The Middle Value)

The median is the middle number in a data set that has been arranged in numerical order.

• How to Calculate: First, sort the numbers from lowest to highest. If there's an odd number of values, the median is the middle one. If there's an even number, the median is the average of the two middle values.
• Example: For {1, 2, 4, 7, 9}, the median is 4. For {1, 2, 4, 7, 9, 10}, the median is (4 + 7) / 2 = 5.5.
• When to Use: The median is a better measure of the center when the data has outliers (e.g., in salary data) because it's not affected by extreme values.

Mode (The Most Frequent Value)

The mode is the number that appears most often in a data set.

• How to Calculate: Count the frequency of each number. The one that appears most is the mode. A data set can have one mode, more than one mode (e.g., "bimodal"), or no mode at all.
• Example: For {1, 4, 7, 4, 9, 2}, the mode is 4. For {1, 4, 7, 9, 2}, there is no mode.
• When to Use: The mode is useful for categorical data (e.g., favorite color) and for identifying the most common value in a set.

Range (The Spread of the Data)

The range is a simple measure of the spread or variability of a data set.

• How to Calculate: Subtract the smallest value from the largest value in the data set.
• Example: For {1, 2, 4, 7, 9}, the range is 9 - 1 = 8.
• When to Use: The range gives a quick sense of the data's spread, but it can be misleading if there are outliers.

Need More Detail?

While these four measures are a great starting point, a full statistical analysis often requires more detail. For a deeper dive that includes standard deviation, variance, and quartiles, check out our comprehensive Statistics Calculator.

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