Data Interpretation and Averages

A data set is a collection of numbers — quiz scores, temperatures, heights, or anything you can measure. Four simple statistics summarize a data set: the mean, the median, the mode, and the range. Each one tells you something different about the numbers, so picking the right one matters.

Mean (the average)

• Add up every value in the data set to get the total.
• Count how many values there are.
• Divide the total by the count: mean = sum / count.
• Example: for 8, 6, 9, 7, 10 — the sum is 40 and the count is 5, so the mean is 40 / 5 = 8.

Median (the middle value)

• First, list the values in order from least to greatest.
• If there is an odd count of values, the median is the single middle number.
• If there is an even count of values, the median is the mean of the two middle numbers.
• Example: for 4, 6, 7, 7, 11 (odd count of 5), the middle value is 7, so the median is 7.

Mode (the most common value)

• The mode is the value that appears most often in the data set.
• A data set can have one mode, more than one mode, or no mode at all if every value appears the same number of times.
• Example: in 3, 3, 7, 9 the value 3 appears twice and the others once, so the mode is 3.

Range (the spread)

• Range tells you how spread out the data is from low to high.
• Subtract the smallest value from the largest value: range = max - min.
• Example: for 2, 5, 9 the largest is 9 and the smallest is 2, so the range is 9 - 2 = 7.
• A small range means the values are close together. A large range means they are far apart.