Mean, Median & Mode

Mean, median, mode, and range are basic tools for describing a set of data. Each one tells a different story about the values in the set, so choosing the right measure matters. In real life, these measures help summarize test scores, prices, sports results, and scientific measurements. A good summary makes patterns easier to see and helps avoid misleading conclusions.

The mean uses every value, so it is useful when data are balanced and there are no extreme outliers. The median shows the middle of an ordered set, so it works well when data are skewed or have unusually large or small values. The mode identifies the most frequent value, which is especially helpful for repeated results or categories. The range measures spread by comparing the largest and smallest values, giving a quick sense of variability.

Key Facts

Mean = (sum of all data values) / (number of data values)
Median is the middle value after the data are arranged in order.
If there are an even number of data values, Median = (two middle values added together) / 2
Mode is the value that appears most often in a data set.
Range = maximum value - minimum value
Use mean for roughly symmetric data, median for skewed data or outliers, mode for most common value, and range for quick spread.

Vocabulary

Mean: The mean is the average found by adding all values and dividing by how many values there are.
Median: The median is the middle value in a data set after the values are put in order.
Mode: The mode is the value that occurs more often than any other value in the data set.
Range: The range is the difference between the largest and smallest values in a data set.
Outlier: An outlier is a value that is much larger or much smaller than the rest of the data.

Common Mistakes to Avoid

Using the mean without checking for outliers, which is wrong because one extreme value can pull the average far away from where most data lie.
Finding the median before sorting the data, which is wrong because the middle only makes sense after the values are arranged in order.
Assuming every data set has exactly one mode, which is wrong because a set can have no mode, one mode, or more than one mode.
Calculating range by subtracting two random numbers, which is wrong because range must be the maximum value minus the minimum value.

Practice Questions

1 Find the mean, median, mode, and range of the data set 4, 6, 6, 8, 10.
2 A student recorded these quiz scores: 72, 75, 78, 80, 95, 100. Calculate the mean, median, and range.
3 A town reports home prices with a few extremely expensive houses far above the rest. Which measure, mean or median, would better represent a typical home price, and why?